Image under Subset of Relation is Subset of Image under Relation/Corollary

Theorem
Let $S$ and $T$ be sets.

Let $\RR_1 \subseteq S \times T$ be a relation in $S \times T$.

Let $\RR_2 \subseteq \RR_1$.

Let $x \in S$.

Then:
 * $\map {\RR_2} x \subseteq \map {\RR_1} x$

where $\map {\RR_1} x$ denotes the image of $x$ under $\RR_1$.