Ultraconnected Space is T4

Theorem
Let $T = \left({X, \vartheta}\right)$ be a topological space which is ultraconnected.

Then $T$ is a $T_4$ space.

Proof
$T = \left({X, \vartheta}\right)$ is a $T_4$ space iff, for any two disjoint closed sets $A, B \subseteq X$, there exist disjoint open sets $U, V \in \vartheta$ containing $A$ and $B$ respectively.

But as no two closed sets of an ultraconnected space are disjoint, it follows that $T_4$-ness follows vacuously.