Irrational Numbers form G-Delta Set in Reals

Theorem
Let $\R \setminus \Q$ denote the set of irrational numbers.

Let $\struct {\R, \tau}$ denote the real number line under the usual (Euclidean) topology.

Then $\R \setminus \Q$ forms a $G_\delta$ set in $\R$.

Proof
The result follows from Rational Numbers are Countably Infinite.