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Theorem nprrel 4329
 Description: No proper class is related to anything via any relation. (Contributed by Roy F. Longton, 30-Jul-2005.)
Hypotheses
Ref Expression
nprrel.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 nprrel.1 . . 3 Rel 𝑅
32brrelexi 4327 . 2 (A𝑅BA V)
41, 3mto 587 1 ¬ A𝑅B
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   ∈ wcel 1390  Vcvv 2551   class class class wbr 3755  Rel wrel 4293 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866  ax-pow 3918  ax-pr 3935 This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-pw 3353  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756  df-opab 3810  df-xp 4294  df-rel 4295 This theorem is referenced by: (None)
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