Inverse of Subset of Relation is Subset of Inverse

Theorem
Let $S$ and $T$ be sets

Let $\mathcal R_1 = S \times T$ be a relation on $S \times T$.

Let $\mathcal R_2 \subseteq \mathcal R_1$.

Then:
 * $\mathcal R_2^{-1} \subseteq \mathcal R_1^{-1}$

where $\mathcal R_1^{-1}$ denotes the inverse of $\mathcal R_1$.

Proof
The result follows by definition of subset.