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Theorem axpow3 4191
 Description: A variant of the Axiom of Power Sets ax-pow 4188. For any set , there exists a set whose members are exactly the subsets of i.e. the power set of . Axiom Pow of [BellMachover] p. 466. (Contributed by NM, 4-Jun-2006.)
Assertion
Ref Expression
axpow3
Distinct variable group:   ,,

Proof of Theorem axpow3
StepHypRef Expression
1 axpow2 4190 . . 3
21bm1.3ii 4144 . 2
3 bicom 191 . . . 4
43albii 1553 . . 3
54exbii 1569 . 2
62, 5mpbir 200 1
 Colors of variables: wff set class Syntax hints:   wb 176  wal 1527  wex 1528   wcel 1684   wss 3152 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-pow 4188 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-in 3159  df-ss 3166
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