P-adic Norm of p-adic Number is Power of p

Theorem
Let $p$ be a prime number.

Let $\struct {\Q_p, \norm {\,\cdot\,}_p}$ be the $p$-adic numbers.

Let $x \in \Q_p: x \ne 0$.

Then:
 * $\exists v \in \Z: \norm x_p = p^{-v}$