Common Divisor Divides Integer Combination/Corollary

Corollary to Common Divisor Divides Integer Combination
Let $c$ be a common divisor of two integers $a$ and $b$.

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

Then:
 * $c \divides \paren {a + b}$

Proof
From Common Divisor Divides Integer Combination:


 * $\forall p, q \in \Z: c \divides \paren {p a + q b}$

The result follows by setting $p = q = 1$.