diff --git a/stdlib/2/__builtin__.pyi b/stdlib/2/__builtin__.pyi
index a681ab626..06222d338 100644
--- a/stdlib/2/__builtin__.pyi
+++ b/stdlib/2/__builtin__.pyi
@@ -689,8 +689,8 @@ bytes = str
 NotImplemented = ...  # type: Any
 
 def abs(n: SupportsAbs[_T]) -> _T: ...
-def all(i: Iterable) -> bool: ...
-def any(i: Iterable) -> bool: ...
+def all(i: Iterable[object]) -> bool: ...
+def any(i: Iterable[object]) -> bool: ...
 def bin(number: int) -> str: ...
 def callable(o: object) -> bool: ...
 def chr(code: int) -> str: ...
diff --git a/stdlib/3/builtins.pyi b/stdlib/3/builtins.pyi
index 1958b1270..43b42bc97 100644
--- a/stdlib/3/builtins.pyi
+++ b/stdlib/3/builtins.pyi
@@ -759,8 +759,8 @@ class property:
 NotImplemented = ...  # type: Any
 
 def abs(n: SupportsAbs[_T]) -> _T: ...
-def all(i: Iterable) -> bool: ...
-def any(i: Iterable) -> bool: ...
+def all(i: Iterable[object]) -> bool: ...
+def any(i: Iterable[object]) -> bool: ...
 def ascii(o: object) -> str: ...
 def bin(number: int) -> str: ...
 def callable(o: object) -> bool: ...