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Theorem brv 30656
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 4667 . 2  |-  <. A ,  B >.  e.  _V
2 df-br 4406 . 2  |-  ( A _V B  <->  <. A ,  B >.  e.  _V )
31, 2mpbir 213 1  |-  A _V B
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1889   _Vcvv 3047   <.cop 3976   class class class wbr 4405
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-5 1760  ax-6 1807  ax-7 1853  ax-9 1898  ax-10 1917  ax-11 1922  ax-12 1935  ax-13 2093  ax-ext 2433  ax-sep 4528  ax-nul 4537  ax-pr 4642
This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 988  df-tru 1449  df-ex 1666  df-nf 1670  df-sb 1800  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2583  df-ne 2626  df-v 3049  df-dif 3409  df-un 3411  df-in 3413  df-ss 3420  df-nul 3734  df-if 3884  df-sn 3971  df-pr 3973  df-op 3977  df-br 4406
This theorem is referenced by:  brsset  30668  brtxpsd  30673  dffun10  30693  elfuns  30694  dfint3  30731  brub  30733
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