Intersection of Exteriors contains Exterior of Union

Theorem
Let $T$ be a topological space.

Let $\mathbb H$ be a set of subsets of $T$.

That is, let $\mathbb H \subseteq \powerset T$ where $\powerset T$ is the power set of $T$.

Then:
 * $\displaystyle \paren {\bigcup_{H \mathop \in \mathbb H} H}^e \subseteq \bigcap_{H \mathop \in \mathbb H} H^e $

where $H^e$ denotes the exterior of $H$.

Proof
In the following, $H^\circ$ denotes the interior of the set $H$.