Common Divisor Divides Integer Combination/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 $c$ divides any integer combination of $a$ and $b$:


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

Proof
We have that the Integers form Integral Domain.

The result then follows from Common Divisor in Integral Domain Divides Linear Combination.