Common Divisor Divides Difference/Proof 1

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:
 * $c \mathop \backslash \left({a - b}\right)$

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

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

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