Editing Axiom of power set (section)

== Formal statement ==
The subset relation <math>\subseteq</math> is not a [[primitive notion]] in [[formal set theory]] and is not used in the formal language of the Zermelo–Fraenkel axioms. Rather, the subset relation <math>\subseteq</math> is defined in terms of [[set membership]], <math>\in</math>. Given this, in the [[formal language]] of the Zermelo–Fraenkel axioms, the axiom of power set reads:
:<math>\forall x \, \exists y \, \forall z \, [z \in y \iff \forall w \, (w \in z \Rightarrow w \in x)]</math>
where ''y'' is the power set of ''x'', ''z'' is any element of ''y'', ''w'' is any member of ''z''.

In English, this says:
:[[Given any]] [[Set (mathematics)|set]] ''x'', [[Existential quantification|there is]] a set ''y'' [[such that]], given any set ''z'', this set ''z'' is a member of ''y'' [[if and only if]] every element of ''z'' is also an element of ''x''.