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Theorem brv 29092
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 4706 . 2  |-  <. A ,  B >.  e.  _V
2 df-br 4443 . 2  |-  ( A _V B  <->  <. A ,  B >.  e.  _V )
31, 2mpbir 209 1  |-  A _V B
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1762   _Vcvv 3108   <.cop 4028   class class class wbr 4442
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-9 1766  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1963  ax-ext 2440  ax-sep 4563  ax-nul 4571  ax-pr 4681
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 970  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2448  df-cleq 2454  df-clel 2457  df-nfc 2612  df-ne 2659  df-v 3110  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3781  df-if 3935  df-sn 4023  df-pr 4025  df-op 4029  df-br 4443
This theorem is referenced by:  brsset  29104  brtxpsd  29109  dffun10  29129  elfuns  29130  dfint3  29167  brub  29169
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