Closed Subset of Real Number Line is G-Delta

Theorem
Let $\left({\R, \tau_d}\right)$ be the real number line under the Euclidean metric considered as a topological space.

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.