Supertransitive class

In set theory, a supertransitive class is a transitive class which includes as a subset the power set of each of its elements.

Formally, let A be a transitive class. Then A is supertransitive if and only if
 * $$(\forall x)(x\in A \to \mathcal{P}(x) \subseteq A).$$

Here P(x) denotes the power set of x.