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Theorem axpow2 4467
 Description: A variant of the Axiom of Power Sets ax-pow 4465 using subset notation. Problem in [BellMachover] p. 466. (Contributed by NM, 4-Jun-2006.)
Assertion
Ref Expression
axpow2
Distinct variable group:   ,,

Proof of Theorem axpow2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ax-pow 4465 . 2
2 dfss2 3340 . . . . 5
32imbi1i 325 . . . 4
43albii 1610 . . 3
54exbii 1634 . 2
61, 5mpbir 209 1
 Colors of variables: wff setvar class Syntax hints:   wi 4  wal 1367  wex 1586   wss 3323 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2419  ax-pow 4465 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2425  df-cleq 2431  df-clel 2434  df-in 3330  df-ss 3337 This theorem is referenced by:  axpow3  4468  pwex  4470
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