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Theorem axpow3 4085
 Description: A variant of the Axiom of Power Sets ax-pow 4082. 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 4084 . . 3
21bm1.3ii 4041 . 2
3 bicom 193 . . . 4
43albii 1554 . . 3
54exbii 1580 . 2
62, 5mpbir 202 1
 Colors of variables: wff set class Syntax hints:   wb 178  wal 1532  wex 1537   wcel 1621   wss 3078 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234  ax-sep 4038  ax-pow 4082 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-in 3085  df-ss 3089
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