Definition:Slowly Well-Ordered Class under Subset Relation

Definition
Let $N$ be a class.

Let $N$ be well-ordered under the subclass relation such that the following $3$ conditions hold:

Then $N$ is slowly well-ordered under the subclass relation.

Also known as
Some sources do not hyphenate, and have well ordered for well-ordered.

Some sources refer to under inclusion for under the subclass relation.