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Theorem elqsg 6948
 Description: Closed form of elqs 6949. (Contributed by Rodolfo Medina, 12-Oct-2010.)
Assertion
Ref Expression
elqsg
Distinct variable groups:   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem elqsg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqeq1 2441 . . 3
21rexbidv 2718 . 2
3 df-qs 6903 . 2
42, 3elab2g 3076 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652   wcel 1725  wrex 2698  cec 6895  cqs 6896 This theorem is referenced by:  elqs  6949  elqsi  6950  ecelqsg  6951  elpi1  19062  prtlem11  26706 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  df-qs 6903
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