MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax-pow Unicode version

Axiom ax-pow 4493
Description: Axiom of Power Sets. An axiom of Zermelo-Fraenkel set theory. It states that a set exists that includes the power set of a given set i.e. contains every subset of . The variant axpow2 4495 uses explicit subset notation. A version using class notation is pwex 4498. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
ax-pow
Distinct variable group:   , , ,

Detailed syntax breakdown of Axiom ax-pow
StepHypRef Expression
1 vw . . . . . . 7
2 vz . . . . . . 7
31, 2wel 1733 . . . . . 6
4 vx . . . . . . 7
51, 4wel 1733 . . . . . 6
63, 5wi 4 . . . . 5
76, 1wal 1564 . . . 4
8 vy . . . . 5
92, 8wel 1733 . . . 4
107, 9wi 4 . . 3
1110, 2wal 1564 . 2
1211, 8wex 1565 1
Colors of variables: wff set class
This axiom is referenced by:  zfpow  4494  axpow2  4495
  Copyright terms: Public domain W3C validator