Subset of Well-Ordered Set is Well-Ordered/Proof 3

Proof
Let $V$ be a basic universe.

By definition of basic universe, $S$ and $T$ are all elements of $V$.

By the Axiom of Transitivity, $S$ and $T$ are both classes.

Thus $T$ is a subclass of $S$.

We have that $\preceq$ is a well-ordering on $S$.

So from Subclass of Well-Ordered Class is Well-Ordered, $\preceq'$ is a well-ordering on $T$.

Hence the result.