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Theorem brvdif2 34655
 Description: Binary relation with universal complement. (Contributed by Peter Mazsa, 14-Jul-2018.)
Assertion
Ref Expression
brvdif2 (𝐴(V ∖ 𝑅)𝐵 ↔ ¬ ⟨𝐴, 𝐵⟩ ∈ 𝑅)

Proof of Theorem brvdif2
StepHypRef Expression
1 brvdif 34654 . 2 (𝐴(V ∖ 𝑅)𝐵 ↔ ¬ 𝐴𝑅𝐵)
2 df-br 4887 . 2 (𝐴𝑅𝐵 ↔ ⟨𝐴, 𝐵⟩ ∈ 𝑅)
31, 2xchbinx 326 1 (𝐴(V ∖ 𝑅)𝐵 ↔ ¬ ⟨𝐴, 𝐵⟩ ∈ 𝑅)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ↔ wb 198   ∈ wcel 2106  Vcvv 3397   ∖ cdif 3788  ⟨cop 4403   class class class wbr 4886 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 2054  ax-9 2115  ax-10 2134  ax-11 2149  ax-12 2162  ax-ext 2753  ax-sep 5017  ax-nul 5025  ax-pr 5138 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 2763  df-cleq 2769  df-clel 2773  df-nfc 2920  df-v 3399  df-dif 3794  df-un 3796  df-in 3798  df-ss 3805  df-nul 4141  df-if 4307  df-sn 4398  df-pr 4400  df-op 4404  df-br 4887 This theorem is referenced by: (None)
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