Have you ever seen statements such as "for every epsilon there is a delta such that the following ... holds"? The axiom of choice implies that in those cases th

Have you ever seen statements such as "for every epsilon there is a delta such that the following ... holds"? The axiom of choice implies that in those cases the delta can be supplied by some function of epsilon. It can't be proven that such a function exists in ordinary ZF (even if you can prove that statement with epsilon and delta).