Image 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 $\Img \RR$ denote the image of $\RR$.

Then:
 * $\ds \Img \RR \subseteq \map \bigcup {\bigcup \RR}$

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

Proof
But then:

Also: