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Theorem nprrel 5726
Description: No proper class is related to anything via any relation. (Contributed by Roy F. Longton, 30-Jul-2005.)
Hypotheses
Ref Expression
nprrel12.1 Rel 𝑅
nprrel.2 ¬ 𝐴 ∈ V
Assertion
Ref Expression
nprrel ¬ 𝐴𝑅𝐵

Proof of Theorem nprrel
StepHypRef Expression
1 nprrel.2 . 2 ¬ 𝐴 ∈ V
2 nprrel12.1 . . 3 Rel 𝑅
32brrelex1i 5723 . 2 (𝐴𝑅𝐵𝐴 ∈ V)
41, 3mto 196 1 ¬ 𝐴𝑅𝐵
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wcel 2098  Vcvv 3466   class class class wbr 5139  Rel wrel 5672
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695  ax-sep 5290  ax-nul 5297  ax-pr 5418
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-ral 3054  df-rex 3063  df-rab 3425  df-v 3468  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-nul 4316  df-if 4522  df-sn 4622  df-pr 4624  df-op 4628  df-br 5140  df-opab 5202  df-xp 5673  df-rel 5674
This theorem is referenced by: (None)
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