**Corollary**: (The cancellation property of integer
multiplication) If a, b, and c are integers with a not zero and ab =
ac, then b = c.

**Proof**: Assume that ab = ac but a is not 0. Then

Factor out an a from both terms.

We now use the fact that if a product is 0 then one of the factors is 0. We have assumed that a is not 0, so we must conclude that

or