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Theorem brrelex1i 4582
Description: The first argument of a binary relation exists. (An artifact of our ordered pair definition.) (Contributed by NM, 4-Jun-1998.)
Hypothesis
Ref Expression
brrelexi.1  |-  Rel  R
Assertion
Ref Expression
brrelex1i  |-  ( A R B  ->  A  e.  _V )

Proof of Theorem brrelex1i
StepHypRef Expression
1 brrelexi.1 . 2  |-  Rel  R
2 brrelex1 4578 . 2  |-  ( ( Rel  R  /\  A R B )  ->  A  e.  _V )
31, 2mpan 420 1  |-  ( A R B  ->  A  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1480   _Vcvv 2686   class class class wbr 3929   Rel wrel 4544
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-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-pow 4098  ax-pr 4131
This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-pw 3512  df-sn 3533  df-pr 3534  df-op 3536  df-br 3930  df-opab 3990  df-xp 4545  df-rel 4546
This theorem is referenced by:  nprrel  4584  vtoclr  4587  opeliunxp2  4679  ideqg  4690  issetid  4693  fvmptss2  5496  opeliunxp2f  6135  brtpos2  6148  brdomg  6642  ctex  6647  isfi  6655  en1uniel  6698  xpdom2  6725  xpdom1g  6727  xpen  6739  isbth  6855  djudom  6978  cc3  7083  aprcl  8415  climcl  11058  climi  11063  climrecl  11100  structex  11981
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