Intersection of Doubleton

Theorem
Let $x$ and $y$ be sets.

Let $\set {x, y}$ be a doubleton.

Then $\bigcap \set {x, y}$ is a set such that:
 * $\bigcap \set {x, y} = x \cap y$

Proof
From Intersection of Non-Empty Class is Set it follows that $x \cap y$ is a set.