Restriction of Mapping to Image is Surjection

Theorem
By restricting the range of any mapping to its image, it can be considered as an surjection. That is:

$$f: \mathrm{Dom} \left({f}\right) \to \mathrm{Im} \left({f}\right)$$ is a surjection.

Proof
The fact that $$f: \mathrm{Dom} \left({f}\right) \to \mathrm{Im} \left({f}\right)$$ is a surjection follows directly from Surjection iff Image equals Range.