Multiple of Divisor Divides Multiple/Proof 1

Theorem
Let $a, b, c \in \Z$.

Let:
 * $a \mathop \backslash b$

where $\backslash$ denotes divisibility.

Then:
 * $a c \mathop \backslash b c$

Proof
We have that Integers form Integral Domain.

The result then follows from Multiple of Divisor in Integral Domain Divides Multiple.