Interior of Finite Intersection equals Intersection of Interiors

Theorem
Let $T$ be a topological space.

Let $n \in \N$.

Let:
 * $\forall i \in \set {1, 2, \dotsc, n}: H_i \subseteq T$

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

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

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