P-adic Norm satisfies Non-Archimedean Norm Axioms

Theorem
Let $p$ be a prime number.

Let $\struct {\Q_p, \norm {\,\cdot\,}_p}$ be the $p$-adic numbers with $p$-adic norm $\norm {\,\cdot\,}_p : \Q_p \to \R_{\ge 0}$.

Then $\norm {\,\cdot\,}_p$ satisfies the non-Archimedean norm axioms:

Proof
From P-adic Numbers form Non-Archimedean Valued Field:
 * $\struct {\Q_p, \norm {\,\cdot\,}_p}$ is a non-Archimedean norm