Interior of Finite Intersection equals Intersection of Interiors

Theorem
Let $T$ be a topological space.

Let $n \in \N$.

Let $\forall i \in \left[{1. . n}\right]: H_i \subseteq T$.

Then:
 * $\displaystyle \left({\bigcap_{i=1}^n H_i}\right)^\circ = \bigcap_{i=1}^n H_i^\circ$

where $H_i^\circ$ denotes the interior of $H_i$.

Proof
In the following, $H_i^-$ denotes the closure of the set $H_i$.