Zorn's Lemma/Formulation 2

Theorem
Let $\struct {S, \preceq}, S \ne \O$ be a non-empty ordered set

Let $T \subseteq \powerset S$ be the set of subsets of $S$ that are totally ordered set by $\preceq$.

Then every element of $T$ is a subset of a maximal element of $T$ under the subset relation.

That is, $T$ is of type $M$.