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Theorem brv 25443
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 4370 . 2  |-  <. A ,  B >.  e.  _V
2 df-br 4156 . 2  |-  ( A _V B  <->  <. A ,  B >.  e.  _V )
31, 2mpbir 201 1  |-  A _V B
Colors of variables: wff set class
Syntax hints:    e. wcel 1717   _Vcvv 2901   <.cop 3762   class class class wbr 4155
This theorem is referenced by:  brsset  25455  brtxpsd  25460  dffun10  25479  elfuns  25480
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2370  ax-sep 4273  ax-nul 4281  ax-pr 4346
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2376  df-cleq 2382  df-clel 2385  df-nfc 2514  df-ne 2554  df-v 2903  df-dif 3268  df-un 3270  df-in 3272  df-ss 3279  df-nul 3574  df-if 3685  df-sn 3765  df-pr 3766  df-op 3768  df-br 4156
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