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Theorem brrelex1i 4552
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 4548 . 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 1465   _Vcvv 2660   class class class wbr 3899   Rel wrel 4514
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-14 1477  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099  ax-sep 4016  ax-pow 4068  ax-pr 4101
This theorem depends on definitions:  df-bi 116  df-3an 949  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-ral 2398  df-rex 2399  df-v 2662  df-un 3045  df-in 3047  df-ss 3054  df-pw 3482  df-sn 3503  df-pr 3504  df-op 3506  df-br 3900  df-opab 3960  df-xp 4515  df-rel 4516
This theorem is referenced by:  nprrel  4554  vtoclr  4557  opeliunxp2  4649  ideqg  4660  issetid  4663  fvmptss2  5464  opeliunxp2f  6103  brtpos2  6116  brdomg  6610  ctex  6615  isfi  6623  en1uniel  6666  xpdom2  6693  xpdom1g  6695  xpen  6707  isbth  6823  djudom  6946  aprcl  8376  climcl  11019  climi  11024  climrecl  11061  structex  11898
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