Discrete Space is Fully Normal

Theorem
Let $T = \left({S, \tau}\right)$ be a discrete topological space.

Then $T$ is fully normal.

Proof
We have that a Discrete Space is fully $T_4$.

Then we note that from Discrete Space satisfies all Separation Properties, a discrete space is a $T_1$ (Fréchet) space.

Therefore, by definition, $T$ is fully normal.