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.

$\blacksquare$