Domain of Relation is Subclass of Union of Union of Relation

Theorem
Let $V$ be a basic universe.

Let $\RR \subseteq V \times V$ be a relation.

Let $\Dom \RR$ denote the domain of $\RR$.

Then:
 * $\Dom \RR \subseteq \map \bigcup {\bigcup \RR}$

where $\bigcup \RR$ denotes the union of $\RR$.

Proof
From Union of Union of Relation is Union of Domain with Image:


 * $\map \bigcup {\bigcup \RR} = \Dom \RR \cup \Img \RR$

The result follows from Class is Subclass of Union.