Bijection iff Left and Right Cancellable

Theorem
Let $f$ be a mapping.

Then $f$ is a bijection iff $f$ is both left cancellable and right cancellable.

Proof
Follows directly from:
 * Injection iff Left Cancellable: $f$ is an injection iff $f$ is left cancellable
 * Surjection iff Right Cancellable: $f$ is a surjection iff $f$ is right cancellable.