Local Basis of P-adic Number

Theorem
Let $p$ be a prime number.

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

Let $\Z_p$ be the $p$-adic integers.

Let $a \in \Q_p$.

Then the set $\set {a + p^n \Z_p: n \in Z}$ is a local basis of $a$ consisting of clopen sets.