Cartesian Product of Preimage with Image of Relation is Correspondence

Theorem
Let $\mathcal R$ be a relation.

Let $A = \operatorname{Im}^{-1} \left ({\mathcal R}\right)$ and let $B = \operatorname{Im} \left ({\mathcal R}\right)$.

Then $\mathcal R \restriction_{A \times B}$ is a correspondence.