Power Set is Filter in Lattice of Power Set

Theorem
Let $X$ be a set.

Let $L = \left({\mathcal P\left({X}\right), \cup, \cap, \subseteq}\right)$ be a inclusion lattice of power set of $X$.

Then $\mathcal P\left({X}\right)$ is a filter on $L$.

Filtered
Let $x, y \in \mathcal P\left({X}\right)$.