Image is Subset of Codomain/Corollary 1

Theorem
Let $$\mathcal{R} = S \times T$$ be a relation.

The image of $$\mathcal{R}$$ is a subset of the range of $$\mathcal{R}$$:

$$\mathrm{Im} \left({\mathcal{R}}\right) \subseteq \mathrm{Rng} \left ({\mathcal{R}}\right)$$.