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Theorem breldm 4755
 Description: Membership of first of a binary relation in a domain. (Contributed by NM, 30-Jul-1995.)
Hypotheses
Ref Expression
opeldm.1
opeldm.2
Assertion
Ref Expression
breldm

Proof of Theorem breldm
StepHypRef Expression
1 df-br 3940 . 2
2 opeldm.1 . . 3
3 opeldm.2 . . 3
42, 3opeldm 4754 . 2
51, 4sylbi 120 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 2112  cvv 2691  cop 3537   class class class wbr 3939   cdm 4551 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2123 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1732  df-clab 2128  df-cleq 2134  df-clel 2137  df-nfc 2272  df-v 2693  df-un 3082  df-sn 3540  df-pr 3541  df-op 3543  df-br 3940  df-dm 4561 This theorem is referenced by:  exse2  4925  funcnv3  5197  dff13  5681  reldmtpos  6162  rntpos  6166  dftpos4  6172  tpostpos  6173  iserd  6467  ntrivcvgap  11378
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