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Theorem brv 5174
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 5473. (Contributed by Scott Fenton, 11-Apr-2012.)
Assertion
Ref Expression
brv 𝐴V𝐵

Proof of Theorem brv
StepHypRef Expression
1 opex 5166 . 2 𝐴, 𝐵⟩ ∈ V
2 df-br 4889 . 2 (𝐴V𝐵 ↔ ⟨𝐴, 𝐵⟩ ∈ V)
31, 2mpbir 223 1 𝐴V𝐵
Colors of variables: wff setvar class
Syntax hints:  wcel 2107  Vcvv 3398  cop 4404   class class class wbr 4888
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-9 2116  ax-10 2135  ax-11 2150  ax-12 2163  ax-ext 2754  ax-sep 5019  ax-nul 5027  ax-pr 5140
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 837  df-3an 1073  df-tru 1605  df-ex 1824  df-nf 1828  df-sb 2012  df-clab 2764  df-cleq 2770  df-clel 2774  df-nfc 2921  df-v 3400  df-dif 3795  df-un 3797  df-in 3799  df-ss 3806  df-nul 4142  df-if 4308  df-sn 4399  df-pr 4401  df-op 4405  df-br 4889
This theorem is referenced by:  brsset  32589  brtxpsd  32594  dffun10  32614  elfuns  32615  dfint3  32652  brub  32654  brvdif  34665
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