Finite Non-Empty Subset of Totally Ordered Set has Smallest and Greatest Elements/Proof 2

Theorem
Let $\left({S, \preceq}\right)$ be a totally ordered set.

Then every finite $T$ such that $\varnothing \subset T \subseteq S$ has both a smallest and a greatest element.

Proof
The result follows from Finite Nonempty Subset of Ordered Set has Maximal and Minimal Elements, Minimal Element of Chain is Smallest Element, and Maximal Element of Chain is Greatest Element.