P-adic Metric on P-adic Numbers is Non-Archimedean Metric/Corollary 1

Theorem
Let $p$ be a prime number.

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

Then:
 * $\forall x, y, z \in R: \norm{x - y}_p \le \max \set{\norm{x - z}_p, \norm{y - z}_p}$