Homomorphism of Ring Subtraction

Theorem
Let $\phi: \struct {R_1, +_1, \circ_1} \to \struct {R_2, +_2, \circ_2}$ be a ring homomorphism.

Then:
 * $\forall a, b \in R_1: \map \phi {a -_1 b} = \map \phi a -_2 \map \phi b$

where $a -_1 b$ denotes subtraction of $b$ from $a$.