Ring Homomorphism Preserves Subrings/Corollary

Corollary to Ring Homomorphism Preserves Subrings
Let $\struct {R_1, +_1, \circ_1}$ and $\struct {R_2, +_2, \circ_2}$ be rings.

The image of a ring homomorphism $\phi: R_1 \to R_2$ is a subring of $R_2$.

Proof
From Null Ring and Ring Itself Subrings, $R_1$ is a subring of itself.

The result then follows from Ring Homomorphism Preserves Subrings.