Definition:Proper Well-Ordering

Definition
Let $V$ be a basic universe.

Let $A$ be a class.

Let $\RR$ be a well-ordering on $A$.

Then $\RR$ is a proper well-ordering :
 * every proper lower section of $A$ is a set.

Also see

 * Well-Ordering on Set is Proper Well-Ordering, showing that this definition is meaningful only in the context of class theory