User blog comment:Hyp cos/Analysis - BEAF, FGH and SGH (part 3)/@comment-24509095-20140626092059/@comment-25418284-20140628073939

@Iko no. a = b most certainly implies that f(a) = f(b), which I believe is a consequence of the Axiom Schema of Replacement and the Axiom of Extension. (The fallacy of the converse would be that f(a) = f(b) implies a = b, which is invalid logic.) If you want to dispute this, then you're disputing Zermelo-Fraenkel set theory.