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Theorem axpow3 3958
 Description: A variant of the Axiom of Power Sets ax-pow 3955. 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 3957 . . 3
21bm1.3ii 3906 . 2
3 bicom 132 . . . 4
43albii 1375 . . 3
54exbii 1512 . 2
62, 5mpbir 138 1
 Colors of variables: wff set class Syntax hints:   wb 102  wal 1257  wex 1397   wss 2945 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-14 1421  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-sep 3903  ax-pow 3955 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-in 2952  df-ss 2959 This theorem is referenced by: (None)
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