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Theorem brv 24417
Description: The binary relationship over  _V always holds. (Contributed by Scott Fenton, 11-Apr-2012.)
Assertion
Ref Expression
brv  |-  A _V B

Proof of Theorem brv
StepHypRef Expression
1 opex 4237 . 2  |-  <. A ,  B >.  e.  _V
2 df-br 4024 . 2  |-  ( A _V B  <->  <. A ,  B >.  e.  _V )
31, 2mpbir 200 1  |-  A _V B
Colors of variables: wff set class
Syntax hints:    e. wcel 1684   _Vcvv 2788   <.cop 3643   class class class wbr 4023
This theorem is referenced by:  brsset  24429  brtxpsd  24434  dffun10  24453  elfuns  24454
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024
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