Euclid's Lemma for Prime Divisors

Lemma
Let $p$ be a prime number.

Let $a$ and $b$ be integers such that:
 * $p \mathop \backslash a b$

where $\backslash$ means is a divisor of.

Then $p \mathop \backslash a$ or $p \mathop \backslash b$.

Also see
Some sources use this property to define a prime number.