Definition:Well-Ordering/Class Theory

Definition
Let $V$ be a basic universe.

Let $\RR \subseteq V \times V$ be a relation.

Let $A \subseteq V$ be a subclass of $V$.

Let the restriction of $\RR$ to $A$ be a total ordering on $A$.

Then $\RR$ is a well-ordering every non-empty subclass of $A$ has a smallest element under $\RR$.