Image of Union of Nest of Mappings is Union of Class of Images

Theorem
Let $N$ be a nest of mappings.

Let $\bigcup N$ denote the union of $N$.

Then:
 * $\Img {\bigcup N} = \ds \bigcup_{f \mathop \in N} \Img f$

where $\Img f$ denotes the image of $f$.