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Theorem opeldm 5211
Description: Membership of first of an ordered pair in a domain. (Contributed by NM, 30-Jul-1995.)
Hypotheses
Ref Expression
opeldm.1
opeldm.2
Assertion
Ref Expression
opeldm

Proof of Theorem opeldm
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 opeldm.2 . . 3
2 opeq2 4218 . . . 4
32eleq1d 2526 . . 3
41, 3spcev 3201 . 2
5 opeldm.1 . . 3
65eldm2 5206 . 2
74, 6sylibr 212 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  =wceq 1395  E.wex 1612  e.wcel 1818   cvv 3109  <.cop 4035  domcdm 5004
This theorem is referenced by:  breldm  5212  elreldm  5232  relssres  5316  iss  5326  imadmrn  5352  dfco2a  5512  funssres  5633  funun  5635  tz7.48-1  7127  iiner  7402  r0weon  8411  axdc3lem2  8852  uzrdgfni  12069  imasaddfnlem  14925  imasvscafn  14934  gsum2d  16999  gsum2dOLD  17000  dfcnv2  27517  cicsym  32588  bnj1379  33889
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-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-rab 2816  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-br 4453  df-dm 5014
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