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Theorem elqs 6916
 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 6915 . 2
31, 2ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wb 177   wceq 1649   wcel 1721  wrex 2667  cvv 2916  cec 6862  cqs 6863 This theorem is referenced by:  qsss  6924  qsid  6929  erovlem  6959  sylow2blem3  15211  divsabl  15435  cldsubg  18093  divstgplem  18103  prter2  26620 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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