Subset of Well-Ordered Set is Well-Ordered

Theorem
Let $\struct {S, \preceq}$ be a well-ordered set.

Let $T \subseteq S$ be a non-empty subset of $S$.

Let $\preceq'$ be the restriction of $\preceq$ to $T$.

Then the relational structure $\struct {T, \preceq'}$ is a well-ordered set.