Image of Subset is Image of Restriction

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

Let $$X \subseteq S$$.

Let $$f \restriction_X$$ be the restriction of $f$ to $X$.

Then:
 * $$f \left({X}\right) = \operatorname{Rng} \left({f \restriction_X}\right)$$