Definition:Supertransitive Class

Definition
Let $A$ be a class.

$A$ is a supertransitive class iff


 * 1) $A$ is a transitive class.
 * 2) $\forall x \in A: \mathcal P \left({ x }\right) \subseteq A$, that is, if $A$ contains the power set of all of its elements.