Metric Space is Countably Compact iff Sequentially Compact

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

Then $M$ is countably compact iff $M$ is sequentially compact.

Proof
We have that a Metric Space is First-Countable.

Then in a first-countable space, sequential compactness is equivalent to countable compactness.