Proving a known proof involving injection.

grjmmr
trying to learn how to do proofs. So I have A=> B which is injective and E $\subseteq$ B then prove f^-1(f(E)) = E.
So let x $\in$ f^-1(f(E)) => thus f(x) $\in$ f(E) => x$\in$ E

So I have proved that x is a point within E, a subset of A, to me I think I am missing something and have not proved f^-1(f(E)) = E.

any suggestions?