Image of Preimage of Ideal under Ring Epimorphism

Theorem
Let $\phi: \left({R_1, +_1, \circ_1}\right) \to \left({R_2, +_2, \circ_2}\right)$ be a ring epimorphism.

Let $S_2$ be an ideal of $R_2$.

Then:
 * $\phi \left[{\phi^{-1} \left[{S_2}\right]}\right] = S_2$

Proof
As an ideal is a subring, the result Image of Preimage of Subring under Ring Epimorphism applies directly.