Surjection iff Right Cancellable/Necessary Condition/Proof 2

Theorem
Let $f$ be a surjection.

Then $f$ is right cancellable.

Proof
Let $f: X \to Y$ be surjective.

Then from Surjection iff Right Inverse:
 * $\exists g: Y \to X: f \circ g = I_Y$

Suppose $h \circ f = k \circ f$ for two mappings $h: Y \to Z$ and $k: Y \to Z$.

Then:

Thus $f$ is right cancellable.

So surjectivity implies right cancellability.