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Theorem axpow2 4371
 Description: A variant of the Axiom of Power Sets ax-pow 4369 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 4369 . 2
2 dfss2 3329 . . . . 5
32imbi1i 316 . . . 4
43albii 1575 . . 3
54exbii 1592 . 2
61, 5mpbir 201 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1549  wex 1550   wss 3312 This theorem is referenced by:  axpow3  4372  pwex  4374 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-pow 4369 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-in 3319  df-ss 3326
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