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Theorem brv 25714
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 4419 . 2  |-  <. A ,  B >.  e.  _V
2 df-br 4205 . 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 1725   _Vcvv 2948   <.cop 3809   class class class wbr 4204
This theorem is referenced by:  brsset  25726  brtxpsd  25731  dffun10  25751  elfuns  25752  dfint3  25789  brub  25791
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205
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