Metric Space is Weakly Countably Compact iff Countably Compact

Theorem
Let $M = \struct {A, d}$ be a metric space.

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

Proof
From Metric Space fulfils all Separation Axioms, a metric space is a $T_1$ (Fréchet) space.

The result follows from $T_1$ Space is Weakly Countably Compact iff Countably Compact.