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Theorem elrel 5110
Description: A member of a relation is an ordered pair. (Contributed by NM, 17-Sep-2006.)
Assertion
Ref Expression
elrel
Distinct variable group:   , ,

Proof of Theorem elrel
StepHypRef Expression
1 df-rel 5011 . . . 4
21biimpi 194 . . 3
32sselda 3503 . 2
4 elvv 5063 . 2
53, 4sylib 196 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818   cvv 3109  C_wss 3475  <.cop 4035  X.cxp 5002  Relwrel 5009
This theorem is referenced by:  eliunxp  5145  elres  5314  unielrel  5537  frxp  6910  rntpos  6987  gsum2d2lem  17001  dfpo2  29184  fundmpss  29196  sscoid  29563  elfuns  29565  eliunxp2  32923
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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  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-ne 2654  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-opab 4511  df-xp 5010  df-rel 5011
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