Image of Element is Subset

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

Let $\RR \subseteq S \times T$ be a relation.

Let $A \subseteq S$.

Then:
 * $s \in A \implies \map \RR s \subseteq \RR \sqbrk A$

Proof
From Image of Singleton under Relation:
 * $\map \RR s = \RR \sqbrk {\set s}$

From Singleton of Element is Subset:
 * $s \in A \implies \set s \subseteq A$

The result follows from Image of Subset is Subset of Image.