Closed Subset of Real Number Line is G-Delta

Theorem
Let $\struct {\R, \tau_d}$ be the real number line with the usual (Euclidean) topology.

Let $H \subseteq \R$ be a closed subset of $\R$.

Then $H$ is a $G_\delta$ set.

Proof
We have:
 * Real Number Line is Metric Space
 * Closed Set in Metric Space is $G_\delta$

Hence the result.