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Theorem rspcegf 27625
 Description: A version of rspcev 3044 using bound-variable hypotheses instead of distinct variable conditions. (Contributed by Glauco Siliprandi, 20-Apr-2017.)
Hypotheses
Ref Expression
rspcegf.1
rspcegf.2
rspcegf.3
rspcegf.4
Assertion
Ref Expression
rspcegf

Proof of Theorem rspcegf
StepHypRef Expression
1 rspcegf.2 . . . 4
2 rspcegf.3 . . . . . 6
31, 2nfel 2579 . . . . 5
4 rspcegf.1 . . . . 5
53, 4nfan 1846 . . . 4
6 eleq1 2495 . . . . 5
7 rspcegf.4 . . . . 5
86, 7anbi12d 692 . . . 4
91, 5, 8spcegf 3024 . . 3
109anabsi5 791 . 2
11 df-rex 2703 . 2
1210, 11sylibr 204 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550  wnf 1553   wceq 1652   wcel 1725  wnfc 2558  wrex 2698 This theorem is referenced by:  stoweidlem46  27726 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 This theorem depends on definitions:  df-bi 178  df-or 360  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-nfc 2560  df-rex 2703  df-v 2950
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