Common Divisor Divides Difference/Proof 1

Proof
Let $c \divides a \land c \divides b$.

From Common Divisor Divides Integer Combination:
 * $\forall p, q \in \Z: c \divides \paren {p a + q b}$

Putting $p = 1$ and $q = -1$:
 * $c \divides \paren {a - b}$