Metric Space is Weakly Countably Compact iff Countably Compact

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

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

Proof
We have that a metric space is a $T_1$ space.

Then from Weakly Countably Compact T1 Space is Countably Compact, in a $T_1$ (Fréchet) space, weakly countable compactness is equivalent to countable compactness.