Assume f:A->B is a function. Can we show that x[itex]\in[/itex]A iff f(x)[itex]\in[/itex]f(A) using only the axioms of Zermel-Fraenkel set theory and the definition of a function?(adsbygoogle = window.adsbygoogle || []).push({});

the statement is intuitive and obvious. but I want to know if it can be proved rigorously using the axioms and the definitions we have.

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# A simple question that I don't know what I should call it

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