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

Step	Hyp	Ref	Expression
1		elqs.1	. 2
2		elqsg 7382	. 2
3	1, 2	ax-mp 5	1

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