Complement of Universe is Empty Set

Theorem
The complement of the universe is the empty set:

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

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