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Theorem brv 5160
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 5457. (Contributed by Scott Fenton, 11-Apr-2012.)
Assertion
Ref Expression
brv 𝐴V𝐵

Proof of Theorem brv
StepHypRef Expression
1 opex 5152 . 2 𝐴, 𝐵⟩ ∈ V
2 df-br 4873 . 2 (𝐴V𝐵 ↔ ⟨𝐴, 𝐵⟩ ∈ V)
31, 2mpbir 223 1 𝐴V𝐵
Colors of variables: wff setvar class
Syntax hints:  wcel 2166  Vcvv 3413  cop 4402   class class class wbr 4872
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-9 2175  ax-10 2194  ax-11 2209  ax-12 2222  ax-13 2390  ax-ext 2802  ax-sep 5004  ax-nul 5012  ax-pr 5126
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 881  df-3an 1115  df-tru 1662  df-ex 1881  df-nf 1885  df-sb 2070  df-clab 2811  df-cleq 2817  df-clel 2820  df-nfc 2957  df-v 3415  df-dif 3800  df-un 3802  df-in 3804  df-ss 3811  df-nul 4144  df-if 4306  df-sn 4397  df-pr 4399  df-op 4403  df-br 4873
This theorem is referenced by:  brsset  32534  brtxpsd  32539  dffun10  32559  elfuns  32560  dfint3  32597  brub  32599  brvdif  34578
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