Empty Class is Well-Ordered
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Theorem
Let $V$ be a basic universe.
Let $\RR \subseteq V \times V$ be a relation.
Let $\O$ denote the empty class.
Then $\O$ is well-ordered under $\RR$.
Proof
We have that $\O$ is well-ordered under $\RR$ if and only if every non-empty subclass of $\O$ has a smallest element under $\RR$.
But $\O$ has no non-empty subclass.
Hence this condition is satisfied vacuously.
The result follows.
$\blacksquare$