diff --git a/mypy/checkmember.py b/mypy/checkmember.py
index 403153fc4293..a5f543812749 100644
--- a/mypy/checkmember.py
+++ b/mypy/checkmember.py
@@ -531,17 +531,6 @@ def instance_alias_type(alias: TypeAlias,
     return expand_type_by_instance(tp, target)
 
 
-def is_instance_var(var: Var, info: TypeInfo) -> bool:
-    """Return if var is an instance variable according to PEP 526."""
-    return (
-        # check the type_info node is the var (not a decorated function, etc.)
-        var.name in info.names and info.names[var.name].node is var
-        and not var.is_classvar
-        # variables without annotations are treated as classvar
-        and not var.is_inferred
-    )
-
-
 def analyze_var(name: str,
                 var: Var,
                 itype: Instance,
@@ -570,12 +559,7 @@ def analyze_var(name: str,
         t = get_proper_type(expand_type_by_instance(typ, itype))
         result: Type = t
         typ = get_proper_type(typ)
-        if (
-            var.is_initialized_in_class
-            and not is_instance_var(var, info)
-            and isinstance(typ, FunctionLike)
-            and not typ.is_type_obj()
-        ):
+        if var.is_initialized_in_class and isinstance(typ, FunctionLike) and not typ.is_type_obj():
             if mx.is_lvalue:
                 if var.is_property:
                     if not var.is_settable_property:
diff --git a/test-data/unit/check-dataclasses.test b/test-data/unit/check-dataclasses.test
index 80ad554d846c..c51f73f7f655 100644
--- a/test-data/unit/check-dataclasses.test
+++ b/test-data/unit/check-dataclasses.test
@@ -1262,45 +1262,81 @@ reveal_type(A.__dataclass_fields__)  # N: Revealed type is "builtins.dict[builti
 
 [builtins fixtures/dict.pyi]
 
-[case testDataclassCallableFieldAccess]
+[case testDataclassCallableProperty]
 # flags: --python-version 3.7
 from dataclasses import dataclass
 from typing import Callable
 
 @dataclass
 class A:
-    x: Callable[[int], int]
-    y: Callable[[int], int] = lambda i: i
+    foo: Callable[[int], int]
 
-a = A(lambda i:i)
-x: int = a.x(0)
-y: str = a.y(0) # E: Incompatible types in assignment (expression has type "int", variable has type "str")
-reveal_type(a.x)  # N: Revealed type is "def (builtins.int) -> builtins.int"
-reveal_type(a.y)  # N: Revealed type is "def (builtins.int) -> builtins.int"
-reveal_type(A.y)  # N: Revealed type is "def (builtins.int) -> builtins.int"
+def my_foo(x: int) -> int:
+    return x
 
+a = A(foo=my_foo)
+a.foo(1)
+reveal_type(a.foo)  # N: Revealed type is "def (builtins.int) -> builtins.int"
+reveal_type(A.foo)  # N: Revealed type is "def (builtins.int) -> builtins.int"
+[typing fixtures/typing-medium.pyi]
 [builtins fixtures/dataclasses.pyi]
 
-[case testDataclassCallableFieldAssignment]
+[case testDataclassCallableAssignment]
 # flags: --python-version 3.7
 from dataclasses import dataclass
 from typing import Callable
 
 @dataclass
 class A:
-    x: Callable[[int], int]
+    foo: Callable[[int], int]
+
+def my_foo(x: int) -> int:
+    return x
 
-def x(i: int) -> int:
-    return i
-def x2(s: str) -> str:
-    return s
+a = A(foo=my_foo)
 
-a = A(lambda i:i)
-a.x = x
-a.x = x2 # E: Incompatible types in assignment (expression has type "Callable[[str], str]", variable has type "Callable[[int], int]")
+def another_foo(x: int) -> int:
+    return x
+
+a.foo = another_foo
+[builtins fixtures/dataclasses.pyi]
 
+[case testDataclassCallablePropertyWrongType]
+# flags: --python-version 3.7
+from dataclasses import dataclass
+from typing import Callable
+
+@dataclass
+class A:
+    foo: Callable[[int], int]
+
+def my_foo(x: int) -> str:
+    return "foo"
+
+a = A(foo=my_foo)  # E: Argument "foo" to "A" has incompatible type "Callable[[int], str]"; expected "Callable[[int], int]"
+[typing fixtures/typing-medium.pyi]
 [builtins fixtures/dataclasses.pyi]
 
+[case testDataclassCallablePropertyWrongTypeAssignment]
+# flags: --python-version 3.7
+from dataclasses import dataclass
+from typing import Callable
+
+@dataclass
+class A:
+    foo: Callable[[int], int]
+
+def my_foo(x: int) -> int:
+    return x
+
+a = A(foo=my_foo)
+
+def another_foo(x: int) -> str:
+    return "foo"
+
+a.foo = another_foo  # E: Incompatible types in assignment (expression has type "Callable[[int], str]", variable has type "Callable[[int], int]")
+[typing fixtures/typing-medium.pyi]
+[builtins fixtures/dataclasses.pyi]
 
 [case testDataclassFieldDoesNotFailOnKwargsUnpacking]
 # flags: --python-version 3.7
diff --git a/test-data/unit/check-functions.test b/test-data/unit/check-functions.test
index 3f75fc5deb9a..b00aad55b204 100644
--- a/test-data/unit/check-functions.test
+++ b/test-data/unit/check-functions.test
@@ -599,12 +599,12 @@ A().f('') # E: Argument 1 to "f" of "A" has incompatible type "str"; expected "i
 
 
 [case testMethodAsDataAttribute]
-from typing import Any, Callable, ClassVar
+from typing import Any, Callable
 class B: pass
 x = None # type: Any
 class A:
-    f = x # type: ClassVar[Callable[[A], None]]
-    g = x # type: ClassVar[Callable[[A, B], None]]
+    f = x # type: Callable[[A], None]
+    g = x # type: Callable[[A, B], None]
 a = None # type: A
 a.f()
 a.g(B())
@@ -612,38 +612,26 @@ a.f(a) # E: Too many arguments
 a.g()  # E: Too few arguments
 
 [case testMethodWithInvalidMethodAsDataAttribute]
-from typing import Any, Callable, ClassVar
+from typing import Any, Callable
 class B: pass
 x = None # type: Any
 class A:
-    f = x # type: ClassVar[Callable[[], None]]
-    g = x # type: ClassVar[Callable[[B], None]]
+    f = x # type: Callable[[], None]
+    g = x # type: Callable[[B], None]
 a = None # type: A
 a.f() # E: Attribute function "f" with type "Callable[[], None]" does not accept self argument
 a.g() # E: Invalid self argument "A" to attribute function "g" with type "Callable[[B], None]"
 
 [case testMethodWithDynamicallyTypedMethodAsDataAttribute]
-from typing import Any, Callable, ClassVar
+from typing import Any, Callable
 class B: pass
 x = None # type: Any
 class A:
-    f = x # type: ClassVar[Callable[[Any], Any]]
+    f = x # type: Callable[[Any], Any]
 a = None # type: A
 a.f()
 a.f(a) # E: Too many arguments
 
-[case testMethodWithInferredMethodAsDataAttribute]
-from typing import Any
-def m(self: "A") -> int: ...
-
-class A:
-    n = m
-
-a = A()
-reveal_type(a.n())  # N: Revealed type is "builtins.int"
-reveal_type(A.n(a))  # N: Revealed type is "builtins.int"
-A.n()  # E: Too few arguments
-
 [case testOverloadedMethodAsDataAttribute]
 from foo import *
 [file foo.pyi]
@@ -685,35 +673,35 @@ a.g(B())
 a.g(a)   # E: Argument 1 has incompatible type "A[B]"; expected "B"
 
 [case testInvalidMethodAsDataAttributeInGenericClass]
-from typing import Any, TypeVar, Generic, Callable, ClassVar
+from typing import Any, TypeVar, Generic, Callable
 t = TypeVar('t')
 class B: pass
 class C: pass
 x = None # type: Any
 class A(Generic[t]):
-    f = x # type: ClassVar[Callable[[A[B]], None]]
+    f = x # type: Callable[[A[B]], None]
 ab = None # type: A[B]
 ac = None # type: A[C]
 ab.f()
 ac.f()   # E: Invalid self argument "A[C]" to attribute function "f" with type "Callable[[A[B]], None]"
 
 [case testPartiallyTypedSelfInMethodDataAttribute]
-from typing import Any, TypeVar, Generic, Callable, ClassVar
+from typing import Any, TypeVar, Generic, Callable
 t = TypeVar('t')
 class B: pass
 class C: pass
 x = None # type: Any
 class A(Generic[t]):
-    f = x # type: ClassVar[Callable[[A], None]]
+    f = x # type: Callable[[A], None]
 ab = None # type: A[B]
 ac = None # type: A[C]
 ab.f()
 ac.f()
 
 [case testCallableDataAttribute]
-from typing import Callable, ClassVar
+from typing import Callable
 class A:
-    g = None # type: ClassVar[Callable[[A], None]]
+    g = None # type: Callable[[A], None]
     def __init__(self, f: Callable[[], None]) -> None:
         self.f = f
 a = A(None)
diff --git a/test-data/unit/check-functools.test b/test-data/unit/check-functools.test
index 5332454202cc..33653c8d3fbc 100644
--- a/test-data/unit/check-functools.test
+++ b/test-data/unit/check-functools.test
@@ -25,12 +25,12 @@ Ord() >= 1  # E: Unsupported operand types for >= ("Ord" and "int")
 
 [case testTotalOrderingLambda]
 from functools import total_ordering
-from typing import Any, Callable, ClassVar
+from typing import Any, Callable
 
 @total_ordering
 class Ord:
-    __eq__: ClassVar[Callable[[Any, object], bool]] = lambda self, other: False
-    __lt__: ClassVar[Callable[[Any, "Ord"], bool]] = lambda self, other: False
+    __eq__: Callable[[Any, object], bool] = lambda self, other: False
+    __lt__: Callable[[Any, "Ord"], bool] = lambda self, other: False
 
 reveal_type(Ord() < Ord())  # N: Revealed type is "builtins.bool"
 reveal_type(Ord() <= Ord())  # N: Revealed type is "builtins.bool"
diff --git a/test-data/unit/check-selftype.test b/test-data/unit/check-selftype.test
index 7e37276a3f75..a1fa234e6d0d 100644
--- a/test-data/unit/check-selftype.test
+++ b/test-data/unit/check-selftype.test
@@ -366,7 +366,7 @@ reveal_type(x.f)  # N: Revealed type is "builtins.int"
 [builtins fixtures/property.pyi]
 
 [case testSelfTypeProperSupertypeAttribute]
-from typing import Callable, TypeVar, ClassVar
+from typing import Callable, TypeVar
 class K: pass
 T = TypeVar('T', bound=K)
 class A(K):
@@ -374,8 +374,8 @@ class A(K):
     def g(self: K) -> int: return 0
     @property
     def gt(self: T) -> T: return self
-    f: ClassVar[Callable[[object], int]]
-    ft: ClassVar[Callable[[T], T]]
+    f: Callable[[object], int]
+    ft: Callable[[T], T]
 
 class B(A):
     pass
@@ -392,15 +392,15 @@ reveal_type(B().ft())  # N: Revealed type is "__main__.B*"
 [builtins fixtures/property.pyi]
 
 [case testSelfTypeProperSupertypeAttributeTuple]
-from typing import Callable, TypeVar, Tuple, ClassVar
+from typing import Callable, TypeVar, Tuple
 T = TypeVar('T')
 class A(Tuple[int, int]):
     @property
     def g(self: object) -> int: return 0
     @property
     def gt(self: T) -> T: return self
-    f: ClassVar[Callable[[object], int]]
-    ft: ClassVar[Callable[[T], T]]
+    f: Callable[[object], int]
+    ft: Callable[[T], T]
 
 class B(A):
     pass
@@ -450,7 +450,7 @@ reveal_type(X1.ft())  # N: Revealed type is "Type[__main__.X]"
 [builtins fixtures/property.pyi]
 
 [case testSelfTypeProperSupertypeAttributeGeneric]
-from typing import Callable, TypeVar, Generic, ClassVar
+from typing import Callable, TypeVar, Generic
 Q = TypeVar('Q', covariant=True)
 class K(Generic[Q]):
     q: Q
@@ -460,8 +460,8 @@ class A(K[Q]):
     def g(self: K[object]) -> int: return 0
     @property
     def gt(self: K[T]) -> T: return self.q
-    f: ClassVar[Callable[[object], int]]
-    ft: ClassVar[Callable[[T], T]]
+    f: Callable[[object], int]
+    ft: Callable[[T], T]
 
 class B(A[Q]):
     pass
diff --git a/test-data/unit/check-slots.test b/test-data/unit/check-slots.test
index 96e4eba3c966..254aa983f82f 100644
--- a/test-data/unit/check-slots.test
+++ b/test-data/unit/check-slots.test
@@ -361,7 +361,8 @@ a.a = 1
 a.b = custom_obj
 a.c = custom_obj
 a.d = custom_obj
-a.e = custom_obj
+# TODO: Should this be allowed?
+a.e = custom_obj  # E: Cannot assign to a method
 [out]
 [builtins fixtures/tuple.pyi]
 [builtins fixtures/dict.pyi]