Lifting The Exponent Lemma/Lemma

Lemma
Let $x, y \in \Z$ be integers.

Let $p$ be an odd prime.

Let:
 * $p \mathrel \backslash x - y$

and:
 * $p \nmid x y$.

Then
 * $\nu_p \left({x^p - y^p}\right) = \nu_p \left({x - y}\right) + 1$

where $\nu_p$ denotes $p$-adic valuation.