Supertransitive class

In set theory, a supertransitive class is a transitive classAny element of a transitive set must also be its subset. See Definition 7.1 of 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 See Definition 9.8 of Here P(x) denotes the power set of x.P(x) must be a set by axiom of power set, since each element x of a class A must be a set (Theorem 4.6 in Takeuti's text above).