Editing Mostowski collapse lemma (section)

==Statement==
Suppose that ''R'' is a binary relation on a class ''X'' such that
*''R'' is [[binary relation#Relations over a set|set-like]]: ''R''<sup>−1</sup>[''x''] = {''y'' : ''y'' ''R'' ''x''} is a set for every ''x'',
*''R'' is [[well-founded relation|well-founded]]: every nonempty subset ''S'' of ''X'' contains an ''R''-minimal element (i.e. an element ''x'' ∈ ''S'' such that ''R''<sup>−1</sup>[''x''] ∩ ''S'' is empty),
*''R'' is [[axiom of extensionality|extensional]]: ''R''<sup>−1</sup>[''x''] ≠ ''R''<sup>−1</sup>[''y''] for every distinct elements ''x'' and ''y'' of ''X''
The Mostowski collapse lemma states that for every such ''R'' there exists a unique [[transitive set|transitive]] class (possibly [[proper class|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).