Complement of Irreducible Topological Subset is Prime Element

Theorem
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $X$ be an irreducible subset of $S$ such that
 * $X \in \tau$

Let $L = \left({\tau, \preceq}\right)$ be an inclusion ordered set of topology $\tau$.

Then $X$ is prime element in $L$.