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Theorem elqs 7383
 Description: Membership in a quotient set. (Contributed by NM, 23-Jul-1995.)
Hypothesis
Ref Expression
elqs.1
Assertion
Ref Expression
elqs
Distinct variable groups:   ,   ,   ,

Proof of Theorem elqs
StepHypRef Expression
1 elqs.1 . 2
2 elqsg 7382 . 2
31, 2ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  =wceq 1395  e.wcel 1818  E.wrex 2808   cvv 3109  [cec 7328  /.cqs 7329 This theorem is referenced by:  qsss  7391  qsid  7396  erovlem  7426  sylow2blem3  16642  qusabl  16871  cldsubg  20609  qustgplem  20619  prter2  30622 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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