Exterior of Finite Union equals Intersection of Exteriors

Theorem
Let $T$ be a topological space.

Let $n \in \N$.

Let $\forall i \in \closedint 1 n: H_i \subseteq T$.

Then:
 * $\displaystyle \paren {\bigcup_{i \mathop = 1}^n H_i}^e = \bigcap_{i \mathop = 1}^n H_i^e$

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

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