Divisor Divides Multiple/Proof 1

Proof
Let $a \divides b$.

From Integer Divides Zero:
 * $a \divides 0$

Thus $a$ is a common divisor of $b$ and $0$.

From Common Divisor Divides Integer Combination:
 * $\forall p, q \in \Z: a \divides \paren {p \cdot b + q \cdot 0}$

Putting $p = c$ and $q = 1$ (for example):
 * $a \divides \paren {c b + 0}$

Hence the result.