Theorem brv 5415

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 5746. (Contributed by Scott Fenton, 11-Apr-2012.)

Assertion

Ref	Expression
brv	⊢ 𝐴V𝐵

Proof of Theorem brv

Step	Hyp	Ref	Expression
1		opex 5406	. 2 ⊢ ⟨𝐴, 𝐵⟩ ∈ V
2		df-br 5076	. 2 ⊢ (𝐴V𝐵 ↔ ⟨𝐴, 𝐵⟩ ∈ V)
3	1, 2	mpbir 233	1 ⊢ 𝐴V𝐵

Syntax hints:   ∈ wcel 2121  Vcvv 3433  ⟨cop 4564   class class class wbr 5075

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1975  ax-7 2016  ax-8 2123  ax-9 2131  ax-ext 2713  ax-sep 5221  ax-pr 5365

This theorem depends on definitions:  df-bi 209  df-an 398  df-or 855  df-3an 1095  df-tru 1551  df-ex 1788  df-sb 2075  df-clab 2720  df-cleq 2733  df-clel 2816  df-rab 3394  df-v 3435  df-un 3890  df-in 3892  df-ss 3902  df-sn 4559  df-pr 4561  df-op 4565  df-br 5076

This theorem is referenced by:  brsset  36130  brtxpsd  36135  dffun10  36155  elfuns  36156  dfint3  36195  brub  36197  brvdif  38648