Image of Empty Set is Empty Set/Corollary 2

Corollary of Image of Empty Set is Empty Set
Let $S = \O$ and $T \ne \O$.

There is no surjection $f: S \to T$.

Proof
Let $f: S \to T$.

By Image of Empty Set is Empty Set/Corollary 1:
 * $f \sqbrk S = \O$

Thus:
 * $f \sqbrk S \ne T$

and $f$ is not a surjection.