# How does Fraenkel's urelement proof show choice is independent of ZF?

I understand the actual proof Fraenkel gives but I can't see how it proves choice independent of the full ZF because he works in a very restricted universe. Can anyone show how to connect one to the other?

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The proof is that if ZFC+Atoms has a model then ZF+$\lnot$AC+Atoms is consistent.

Therefore we cannot prove the axiom of choice from the axioms of ZF+Atoms.

The removal of atoms did not occur for another 40 years until Cohen developed forcing, and Gödel proved that the axiom of choice does not add contradictions to ZF.

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