Union of Doubleton

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

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

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

Proof
Then, from Axiom of Unions, it follows that $x \cup y$ is a set.