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Theorem brv 5340
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 5649. (Contributed by Scott Fenton, 11-Apr-2012.)
Assertion
Ref Expression
brv 𝐴V𝐵

Proof of Theorem brv
StepHypRef Expression
1 opex 5332 . 2 𝐴, 𝐵⟩ ∈ V
2 df-br 5043 . 2 (𝐴V𝐵 ↔ ⟨𝐴, 𝐵⟩ ∈ V)
31, 2mpbir 233 1 𝐴V𝐵
Colors of variables: wff setvar class
Syntax hints:  wcel 2114  Vcvv 3473  cop 4549   class class class wbr 5042
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 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2177  ax-ext 2792  ax-sep 5179  ax-nul 5186  ax-pr 5306
This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1085  df-tru 1540  df-ex 1781  df-nf 1785  df-sb 2070  df-clab 2799  df-cleq 2813  df-clel 2891  df-nfc 2959  df-v 3475  df-dif 3916  df-un 3918  df-in 3920  df-ss 3930  df-nul 4270  df-if 4444  df-sn 4544  df-pr 4546  df-op 4550  df-br 5043
This theorem is referenced by:  brsset  33358  brtxpsd  33363  dffun10  33383  elfuns  33384  dfint3  33421  brub  33423  brvdif  35558
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