Definition:Well-Ordering/Class Theory

Definition
Let $V$ be a basic universe.

Let $\RR \subseteq V \times V$ be a total ordering.

Then $\RR$ is a well-ordering :
 * every non-empty subclass of $\Field \RR$ has a smallest element under $\RR$

where $\Field \RR$ denotes the field of $\RR$.