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Axiom ax-pow 3918
Description: Axiom of Power Sets. An axiom of Intuitionistic 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 . This is Axiom 8 of [Crosilla] p. "Axioms of CZF and IZF" except (a) unnecessary quantifiers are removed, and (b) Crosilla has a biconditional rather than an implication (but the two are equivalent by bm1.3ii 3869).

The variant axpow2 3920 uses explicit subset notation. A version using class notation is pwex 3923. (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  setvar
2 vz . . . . . . 7  setvar
31, 2wel 1391 . . . . . 6
4 vx . . . . . . 7  setvar
51, 4wel 1391 . . . . . 6
63, 5wi 4 . . . . 5
76, 1wal 1240 . . . 4
8 vy . . . . 5  setvar
92, 8wel 1391 . . . 4
107, 9wi 4 . . 3
1110, 2wal 1240 . 2
1211, 8wex 1378 1
Colors of variables: wff set class
This axiom is referenced by:  zfpow  3919  axpow2  3920
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