diff --git a/mypy/checker.py b/mypy/checker.py
index 2f99b9b4fece7..64b51f5e001a5 100644
--- a/mypy/checker.py
+++ b/mypy/checker.py
@@ -58,7 +58,7 @@
     try_getting_str_literals_from_type, try_getting_int_literals_from_type,
     tuple_fallback, is_singleton_type, try_expanding_sum_type_to_union,
     true_only, false_only, function_type, get_type_vars, custom_special_method,
-    is_literal_type_like,
+    is_literal_type_like, is_truthy_type
 )
 from mypy import message_registry
 from mypy.message_registry import ErrorMessage
@@ -4302,27 +4302,12 @@ def conditional_callable_type_map(self, expr: Expression,
 
         return None, {}
 
-    def _is_truthy_type(self, t: ProperType) -> bool:
-        return (
-            (
-                isinstance(t, Instance) and
-                bool(t.type) and
-                not t.type.has_readable_member('__bool__') and
-                not t.type.has_readable_member('__len__')
-            )
-            or isinstance(t, FunctionLike)
-            or (
-                isinstance(t, UnionType) and
-                all(self._is_truthy_type(t) for t in get_proper_types(t.items))
-            )
-        )
-
     def _check_for_truthy_type(self, t: Type, expr: Expression) -> None:
         if not state.strict_optional:
             return  # if everything can be None, all bets are off
 
         t = get_proper_type(t)
-        if not self._is_truthy_type(t):
+        if not is_truthy_type(t):
             return
 
         def format_expr_type() -> str:
@@ -4686,7 +4671,6 @@ def has_no_custom_eq_checks(t: Type) -> bool:
         original_vartype = type_map[node]
         self._check_for_truthy_type(original_vartype, node)
         vartype = try_expanding_sum_type_to_union(original_vartype, "builtins.bool")
-
         if_type = true_only(vartype)
         else_type = false_only(vartype)
         if_map = (
diff --git a/mypy/test/testtypes.py b/mypy/test/testtypes.py
index 6af1c18145cfe..9fb1f458856bc 100644
--- a/mypy/test/testtypes.py
+++ b/mypy/test/testtypes.py
@@ -409,6 +409,14 @@ def test_true_only_of_union(self) -> None:
         assert not to.items[0].can_be_false
         assert to.items[1] is tup_type
 
+    def test_true_only_of_truthy_type(self) -> None:
+        t = self.fx.d
+        t.type.is_final = True
+        dto = true_only(self.fx.d)
+        assert_equal(self.fx.d, dto)
+        fto = true_only(self.fx.function)
+        assert_equal(self.fx.function, fto)
+
     def test_false_only_of_true_type_is_uninhabited(self) -> None:
         with strict_optional_set(True):
             fo = false_only(self.tuple(AnyType(TypeOfAny.special_form)))
@@ -451,6 +459,13 @@ def test_false_only_of_union(self) -> None:
             assert fo.items[0].can_be_false
             assert fo.items[1] is tup_type
 
+    def test_false_only_of_truthy_type_is_uninhabited(self) -> None:
+        t = self.fx.d
+        t.type.is_final = True
+        with strict_optional_set(True):
+            fo = false_only(t)
+            assert_type(UninhabitedType, fo)
+
     def test_simplified_union(self) -> None:
         fx = self.fx
 
diff --git a/mypy/typeops.py b/mypy/typeops.py
index 88d4bc744bdf8..f6fb1bbdd5d58 100644
--- a/mypy/typeops.py
+++ b/mypy/typeops.py
@@ -397,6 +397,26 @@ def make_simplified_union(items: Sequence[Type],
     return UnionType.make_union(simplified_set, line, column)
 
 
+def is_truthy_type(t: ProperType) -> bool:
+    return (
+        (
+            isinstance(t, Instance) and
+            bool(t.type) and
+            not t.type.has_readable_member('__bool__') and
+            not t.type.has_readable_member('__len__')
+        )
+        or isinstance(t, FunctionLike)
+        or (
+            isinstance(t, UnionType) and
+            all(is_truthy_type(t) for t in get_proper_types(t.items))
+        )
+    )
+
+
+def _is_final_truthy_type(t: ProperType) -> bool:
+    return is_truthy_type(t) and (not isinstance(t, Instance) or t.type.is_final)
+
+
 def _get_type_special_method_bool_ret_type(t: Type) -> Optional[Type]:
     t = get_proper_type(t)
 
@@ -419,7 +439,7 @@ def true_only(t: Type) -> ProperType:
     if not t.can_be_true:
         # All values of t are False-ish, so there are no true values in it
         return UninhabitedType(line=t.line, column=t.column)
-    elif not t.can_be_false:
+    elif not t.can_be_false or _is_final_truthy_type(t):
         # All values of t are already True-ish, so true_only is idempotent in this case
         return t
     elif isinstance(t, UnionType):
@@ -446,7 +466,7 @@ def false_only(t: Type) -> ProperType:
     """
     t = get_proper_type(t)
 
-    if not t.can_be_false:
+    if not t.can_be_false or _is_final_truthy_type(t):
         if state.strict_optional:
             # All values of t are True-ish, so there are no false values in it
             return UninhabitedType(line=t.line)