Common Divisor in Integral Domain Divides Linear Combination

Theorem
Let $c$ be a common divisor of two integers $a$ and $b$.

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

Then $c$ divides any integer combination of $a$ and $b$:


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