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Theorem elqsg 7382
Description: Closed form of elqs 7383. (Contributed by Rodolfo Medina, 12-Oct-2010.)
Assertion
Ref Expression
elqsg
Distinct variable groups:   ,   ,   ,

Proof of Theorem elqsg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqeq1 2461 . . 3
21rexbidv 2968 . 2
3 df-qs 7336 . 2
42, 3elab2g 3248 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  e.wcel 1818  E.wrex 2808  [cec 7328  /.cqs 7329
This theorem is referenced by:  elqs  7383  elqsi  7384  ecelqsg  7385  elpi1  21545  eclclwwlkn0  24831  prtlem11  30607
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-v 3111  df-qs 7336
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