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Theorem brv 30183
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 4652 . 2  |-  <. A ,  B >.  e.  _V
2 df-br 4393 . 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 1840   _Vcvv 3056   <.cop 3975   class class class wbr 4392
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1637  ax-4 1650  ax-5 1723  ax-6 1769  ax-7 1812  ax-9 1844  ax-10 1859  ax-11 1864  ax-12 1876  ax-13 2024  ax-ext 2378  ax-sep 4514  ax-nul 4522  ax-pr 4627
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 974  df-tru 1406  df-ex 1632  df-nf 1636  df-sb 1762  df-clab 2386  df-cleq 2392  df-clel 2395  df-nfc 2550  df-ne 2598  df-v 3058  df-dif 3414  df-un 3416  df-in 3418  df-ss 3425  df-nul 3736  df-if 3883  df-sn 3970  df-pr 3972  df-op 3976  df-br 4393
This theorem is referenced by:  brsset  30195  brtxpsd  30200  dffun10  30220  elfuns  30221  dfint3  30258  brub  30260
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