Multiple of Divisor Divides Multiple/Proof 1

Theorem

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

Let:

$a \divides b$

where $\divides$ denotes divisibility.

Then:

$a c \divides b c$

Proof

We have that Integers form Integral Domain.

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

$\blacksquare$