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Theorem opeldm 5102
 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 4009 . . . 4
32eleq1d 2508 . . 3
41, 3spcev 3049 . 2
5 opeldm.1 . . 3
65eldm2 5097 . 2
74, 6sylibr 205 1
 Colors of variables: wff set class Syntax hints:   wi 4  wex 1551   wceq 1653   wcel 1727  cvv 2962  cop 3841   cdm 4907 This theorem is referenced by:  breldm  5103  elreldm  5123  relssres  5212  iss  5218  imadmrn  5244  dfco2a  5399  funssres  5522  funun  5524  tz7.48-1  6729  iiner  7005  r0weon  7925  axdc3lem2  8362  uzrdgfni  11329  imasaddfnlem  13784  imasvscafn  13793  gsum2d  15577  bnj1379  29300 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-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 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-rab 2720  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-br 4238  df-dm 4917
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