Supertransitive class

In set theory, a supertransitive class is a transitive class^[1] 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

${\displaystyle (\forall x)(x\in A\to {\mathcal {P}}(x)\subseteq A).}$^[2]

Here P(x) denotes the power set of x.^[3]