Domain of Union of Nest of Mappings is Union of Class of Domains

Theorem
Let $N$ be a nest of mappings.

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

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

where $\Dom f$ denotes the domain of $f$.