Empty Set is Well-Ordered

Theorem
Let $S$ be a set.

Let $\RR \subseteq S \times S$ be a relation on $S$.

Let $\O$ denote the empty set.

Let $\RR_\O$ denote the restriction of $\RR$ to $\O$.

Then $\struct {\O, \RR_\O}$ is a well-ordered set.