Common Divisor Divides Difference/Proof 2

Theorem
Let $c$ be a common divisor of two integers $a$ and $b$.

That is:
 * $a, b, c \in \Z: c \mathop \backslash a \land c \mathop \backslash b$

Then:
 * $\forall p, q \in \Z: c \mathop \backslash \left({a - b}\right)$