Sequence of P-adic Integers has Convergent Subsequence

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

Let $\sequence{x_n}$ be a sequence of $p$-adic integers.

Then:
 * there exists a convergent subsequence $\sequence {x_{n_r} }_{r \mathop \in \N}$ of $\sequence{x_n}$