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Theorem brv 5411
Description: Two classes are always in relation by V. This is simply equivalent to 𝐴, 𝐵⟩ ∈ V, and does not imply that V is a relation: see nrelv 5736. (Contributed by Scott Fenton, 11-Apr-2012.)
Assertion
Ref Expression
brv 𝐴V𝐵

Proof of Theorem brv
StepHypRef Expression
1 opex 5403 . 2 𝐴, 𝐵⟩ ∈ V
2 df-br 5090 . 2 (𝐴V𝐵 ↔ ⟨𝐴, 𝐵⟩ ∈ V)
31, 2mpbir 230 1 𝐴V𝐵
Colors of variables: wff setvar class
Syntax hints:  wcel 2105  Vcvv 3441  cop 4578   class class class wbr 5089
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2707  ax-sep 5240  ax-nul 5247  ax-pr 5369
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1781  df-sb 2067  df-clab 2714  df-cleq 2728  df-clel 2814  df-v 3443  df-dif 3900  df-un 3902  df-in 3904  df-ss 3914  df-nul 4269  df-if 4473  df-sn 4573  df-pr 4575  df-op 4579  df-br 5090
This theorem is referenced by:  brsset  34282  brtxpsd  34287  dffun10  34307  elfuns  34308  dfint3  34345  brub  34347  brvdif  36519
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