^Any element of a transitive set must also be its subset. See Definition 7.1 of Zaring W.M., G. Takeuti (1971). Introduction to axiomatic set theory (2nd, rev. ed.). New York: Springer-Verlag.
ISBN0387900241.
^See Definition 9.8 of Zaring W.M., G. Takeuti (1971). Introduction to axiomatic set theory (2nd, rev. ed.). New York: Springer-Verlag.
ISBN0387900241.
^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).