Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  elqsi Structured version   Unicode version

Theorem elqsi 6950
 Description: Membership in a quotient set. (Contributed by NM, 23-Jul-1995.)
Assertion
Ref Expression
elqsi
Distinct variable groups:   ,   ,   ,

Proof of Theorem elqsi
StepHypRef Expression
1 elqsg 6948 . 2
21ibi 233 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  wrex 2698  cec 6895  cqs 6896 This theorem is referenced by:  ectocld  6963  ecoptocl  6986  eroveu  6991  pstmxmet  24284 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rex 2703  df-v 2950  df-qs 6903
 Copyright terms: Public domain W3C validator