Preimage_of_Image_of_Subring_under_Ring_Homomorphism

Let $\phi: \left({R_1, +_1, \circ_1}\right) \to \left({R_2, +_2, \circ_2}\right)$ be a ring homomorphism. Let $K = \ker \left({\phi}\right)$, where $\ker \left({\phi}\right)$ is the kernel of $\phi$. Let $J$ be a subring of $R_1$. Then $\phi^{-1} \left[{\phi \left[{J}\right]}\right] = J + K$