diff --git a/stdlib/builtins.pyi b/stdlib/builtins.pyi
index 56c5a4d28af9..3122cc35d18a 100644
--- a/stdlib/builtins.pyi
+++ b/stdlib/builtins.pyi
@@ -75,6 +75,7 @@ _TBE = TypeVar("_TBE", bound="BaseException")
 _R = TypeVar("_R")  # Return-type TypeVar
 _SupportsNextT = TypeVar("_SupportsNextT", bound=SupportsNext[Any], covariant=True)
 _SupportsAnextT = TypeVar("_SupportsAnextT", bound=SupportsAnext[Any], covariant=True)
+_B = TypeVar("_B", bool, int)
 
 class _SupportsIter(Protocol[_T_co]):
     def __iter__(self) -> _T_co: ...
@@ -702,30 +703,12 @@ class memoryview(Sized, Sequence[int]):
 @final
 class bool(int):
     def __new__(cls: Type[_T], __o: object = ...) -> _T: ...
-    @overload
-    def __and__(self, __x: bool) -> bool: ...
-    @overload
-    def __and__(self, __x: int) -> int: ...
-    @overload
-    def __or__(self, __x: bool) -> bool: ...
-    @overload
-    def __or__(self, __x: int) -> int: ...
-    @overload
-    def __xor__(self, __x: bool) -> bool: ...
-    @overload
-    def __xor__(self, __x: int) -> int: ...
-    @overload
-    def __rand__(self, __x: bool) -> bool: ...
-    @overload
-    def __rand__(self, __x: int) -> int: ...
-    @overload
-    def __ror__(self, __x: bool) -> bool: ...
-    @overload
-    def __ror__(self, __x: int) -> int: ...
-    @overload
-    def __rxor__(self, __x: bool) -> bool: ...
-    @overload
-    def __rxor__(self, __x: int) -> int: ...
+    def __and__(self, __x: _B) -> _B: ...
+    def __or__(self, __x: _B) -> _B: ...
+    def __xor__(self, __x: _B) -> _B: ...
+    def __rand__(self, __x: _B) -> _B: ...
+    def __ror__(self, __x: _B) -> _B: ...
+    def __rxor__(self, __x: _B) -> _B: ...
     def __getnewargs__(self) -> tuple[int]: ...
 
 @final