Theorem (Mostowski’s Collapsing Theorem). Let $r$ be a relation on a set $a$ that is well-founded and extensional. Then there exists a transitive set $b$, adn a bijection $f:a\to b$ such that $(\forall x,y\in a)(x r y⟺f(x)\in f(y))$. Moreover, $b$ and $f$ are unique.