diff --git a/fastapi/routing.py b/fastapi/routing.py
index 8842745bd..13ccf9ab9 100644
--- a/fastapi/routing.py
+++ b/fastapi/routing.py
@@ -1204,7 +1204,7 @@ class APIRouter(routing.Router):
         app.include_router(internal_router)
         ```
         """
-        assert self != router, "Router cannot be the same as parent"
+        assert id(self) != id(router), "Router cannot be the same as parent"
         if prefix:
             assert prefix.startswith("/"), "A path prefix must start with '/'"
             assert not prefix.endswith(