Full Idea
Power Set Axiom: ∀x ∃y ∀z(z ⊂ x → z ∈ y). That is, there is a set y which contains all of the subsets of a given set. Hence we define P(x) = {z : z ⊂ x}.
Gist of Idea
Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y)
Source
Kenneth Kunen (Set Theory [1980], §1.10)
Book Reference
Kunen,Kenneth: 'Set Theory: Introduction to Independence Proofs' [North-Holland 1980], p.29