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Theorem elqsg 6915
 Description: Closed form of elqs 6916. (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 2410 . . 3
21rexbidv 2687 . 2
3 df-qs 6870 . 2
42, 3elab2g 3044 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1649   wcel 1721  wrex 2667  cec 6862  cqs 6863 This theorem is referenced by:  elqs  6916  elqsi  6917  ecelqsg  6918  elpi1  19023  prtlem11  26605 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-rex 2672  df-v 2918  df-qs 6870
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