Union of Set of Ordinals is Ordinal/Corollary

Corollary to Union of Set of Ordinals is Ordinal
Let $y$ be a set.

Let $\On$ be the class of all ordinals.

Let $F: y \to \On$ be a mapping.

Then:


 * $\bigcup \map F y \in \On$

where $\map F y$ is the image of $y$ under $F$.