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

Theorem elrel 5007
 Description: A member of a relation is an ordered pair. (Contributed by NM, 17-Sep-2006.)
Assertion
Ref Expression
elrel
Distinct variable group:   ,,
Allowed substitution hints:   (,)

Proof of Theorem elrel
StepHypRef Expression
1 df-rel 4914 . . . 4
21biimpi 188 . . 3
32sselda 3334 . 2
4 elvv 4965 . 2
53, 4sylib 190 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360  wex 1551   wceq 1653   wcel 1727  cvv 2962   wss 3306  cop 3841   cxp 4905   wrel 4912 This theorem is referenced by:  eliunxp  5041  elres  5210  unielrel  5423  frxp  6485  rntpos  6521  gsum2d2lem  15578  dfpo2  25409  fundmpss  25421  sscoid  25789  elfuns  25791 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-14 1731  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423  ax-sep 4355  ax-nul 4363  ax-pr 4432 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ne 2607  df-v 2964  df-dif 3309  df-un 3311  df-in 3313  df-ss 3320  df-nul 3614  df-if 3764  df-sn 3844  df-pr 3845  df-op 3847  df-opab 4292  df-xp 4913  df-rel 4914
 Copyright terms: Public domain W3C validator