Subset Maps to Subset

Theorem
Let $$f: S \to T$$ be a mapping.

Let $$A, B \subseteq S$$ such that $$A \subseteq B$$.

Then the image of $$A$$ is a subset of the image of $$B$$:


 * $$A \subseteq B \implies f \left({A}\right) \subseteq f \left({B}\right)$$.

Proof
As $$f$$, being a mapping, is also a relation, we use Subset of Image directly.