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Theorem brv 31154
 Description: The binary relationship over V always holds. (Contributed by Scott Fenton, 11-Apr-2012.)
Assertion
Ref Expression
brv 𝐴V𝐵

Proof of Theorem brv
StepHypRef Expression
1 opex 4859 . 2 𝐴, 𝐵⟩ ∈ V
2 df-br 4584 . 2 (𝐴V𝐵 ↔ ⟨𝐴, 𝐵⟩ ∈ V)
31, 2mpbir 220 1 𝐴V𝐵
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 1977  Vcvv 3173  ⟨cop 4131   class class class wbr 4583 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-9 1986  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590  ax-sep 4709  ax-nul 4717  ax-pr 4833 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-br 4584 This theorem is referenced by:  brsset  31166  brtxpsd  31171  dffun10  31191  elfuns  31192  dfint3  31229  brub  31231
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