Not Preceding implies Exists Completely Irreducible Element in Algebraic Lattice

Theorem
Let $L = \left({S, \vee, \wedge, \preceq}\right)$ be a bounded below algebraic lattice.

Let $x, y \in S$ such that
 * $y \npreceq x$

Then
 * $\exists p \in S: p$ is completely irreducible $\land ~x \preceq p \land y \npreceq p$