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Theorem opeldm 4737
 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 3701 . . . 4
32eleq1d 2206 . . 3
41, 3spcev 2775 . 2
5 opeldm.1 . . 3
65eldm2 4732 . 2
74, 6sylibr 133 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1331  wex 1468   wcel 1480  cvv 2681  cop 3525   cdm 4534 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-un 3070  df-sn 3528  df-pr 3529  df-op 3531  df-br 3925  df-dm 4544 This theorem is referenced by:  breldm  4738  elreldm  4760  relssres  4852  iss  4860  imadmrn  4886  dfco2a  5034  funssres  5160  funun  5162  iinerm  6494
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