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.