Can anyone explain what Mostowski collapse lemma is?
The Mostowski collapse lemma states that for any such $R$ there exists a unique transitive class (possibly proper) whose structure under the membership relation is isomorphic to $(X, R)$, and the isomorphism is unique. The isomorphism maps each element $x$ of $X$ to the set of images of elements $y$ of $X$ such that $y R x$ (Jech 2003:69).
What does this mean? This explanation seems very unclear to me.