Metric Space is Perfectly T4

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

Then $M$ is a perfectly $T_4$ space.

Proof
We have that a metric space is $T_4$.

We also have that every closed set in a metric space is a $G_\delta$ set.

Hence the result, by definition of a perfectly $T_4$ space.