Isolated Point of Closure of Subset is Isolated Point of Subset

Theorem
Let $\struct {T, \tau}$ be a topological space.

Let $H \subseteq T$ be a subset of $T$.

Let $\map \cl H$ denote the closure of $H$.

Let $x \in \map \cl H$ be an isolated point of $\map \cl H$.

Then $x$ is also an isolated point of $H$.