Common Divisor Divides Difference/Proof 1

Proof
Let $c \mathrel \backslash a \land c \mathrel \backslash b$.

From Common Divisor Divides Integer Combination:
 * $\forall p, q \in \Z: c \mathrel \backslash \left({p a + q b}\right)$

Putting $p = 1$ and $q = -1$:
 * $c \mathrel \backslash \left({a - b}\right)$