Image of Intersection under Mapping/Proof 2

Proof
As $f$, being a mapping, is also a relation, we can apply Image of Intersection under Relation:


 * $\mathcal R \sqbrk {S_1 \cap S_2} \subseteq \mathcal R \sqbrk {S_1} \cap \mathcal R \sqbrk {S_2}$