Preimage_of_Subring_under_Ring_Homomorphism_is_Subring

Let $\phi: \left({R_1, +_1, \circ_1}\right) \to \left({R_2, +_2, \circ_2}\right)$ be a ring homomorphism. Let $S_2$ be a subring of $R_2$. Then $S_1 = \phi^{-1} \left[{S_2}\right]$ is a subring of $R_1$ such that $\ker \left({\phi}\right) \subseteq S_1$.