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Theorem breldm 4482
Description: Membership of first of a binary relation in a domain. (Contributed by NM, 30-Jul-1995.)
Hypotheses
Ref Expression
opeldm.1  _V
opeldm.2  _V
Assertion
Ref Expression
breldm  R  dom  R

Proof of Theorem breldm
StepHypRef Expression
1 df-br 3756 . 2  R  <. ,  >.  R
2 opeldm.1 . . 3  _V
3 opeldm.2 . . 3  _V
42, 3opeldm 4481 . 2  <. ,  >.  R  dom  R
51, 4sylbi 114 1  R  dom  R
Colors of variables: wff set class
Syntax hints:   wi 4   wcel 1390   _Vcvv 2551   <.cop 3370   class class class wbr 3755   dom cdm 4288
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756  df-dm 4298
This theorem is referenced by:  exse2  4642  funcnv3  4904  dff13  5350  reldmtpos  5809  rntpos  5813  dftpos4  5819  tpostpos  5820  iserd  6068
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