Pseudoprime Element is Prime in Arithmetic Lattice

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

Let $p \in S$.

Then if $p$ is pseudoprime element, then $p$ is prime element.

Proof
By Arithmetic iff Way Below Relation is Multiplicative in Algebraic Lattice:
 * $\ll$ is a multiplicative relation.

Thus by Way Below Relation is Multiplicative implies Pseudoprime Element is Prime:
 * the result holds.