Complement of Empty Set is Universe

Theorem
The complement of the empty set is the universe:


 * $$\mathcal{C} \left({\varnothing}\right) = \mathbb{U}$$

Proof
Substitute $$\mathbb{U}$$ for $$S$$ in $$\mathcal{C}_S \left({\varnothing}\right) = S$$ from Relative Complement of Null.