Empty Class is Supercomplete

Theorem
The empty class is supercomplete.

Proof
Vacuously, every element of $\O$ is also a subclass of $\O$.

Hence $\O$ is transitive by definition.

Vacuously, every subclass of every element of $\O$ is also an element of $\O$.

Hence $\O$ is swelled by definition.

The result follows by definition of supercomplete.