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Also, the profoundly intuitive [http://en.wikipedia.org/wiki/Trichotomy_%28mathematics%29 trichotomy] is equivalent to AC, so be careful what you call controversial. [[User:BenjB|BenjB]] 20:29, 27 January 2008 (EST)
Also, the profoundly intuitive [http://en.wikipedia.org/wiki/Trichotomy_%28mathematics%29 trichotomy] is equivalent to AC, so be careful what you call controversial. [[User:BenjB|BenjB]] 20:29, 27 January 2008 (EST)
Actually, the Axiom of Choice has been proven '''independent''' of ZF, so there is no such transformation of a proof. Otherwise, "prove" AC as follows:
-----------------------------------------------
1. Axiom of Choice | Reason: Axiom of Choice
Then transform it to not need AC.
Result: AC proven in ZF,so ZFC=ZF.
But AC proved independent of ZF.
Therefore, no such transformation exists.
QED
[[User:SamSamson|SamSamson]] 21:50, 8 June 2008 (EDT)