Countably Compact Metric Space is Compact/Proof 1

Theorem
Let $M = \left({A, d}\right)$ be a metric space.

Let $M$ be countably compact.

Then $M$ is compact.

Proof
This follows directly from:
 * Metric Space is First-Countable
 * Countably Compact First-Countable Space is Sequentially Compact
 * Sequentially Compact Metric Space is Totally Bounded
 * Totally Bounded Metric Space is Second-Countable
 * Second-Countable Space is Compact iff Countably Compact