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Theorem intnexr 3896
 Description: If a class intersection is the universe, it is not a set. In classical logic this would be an equivalence. (Contributed by Jim Kingdon, 27-Aug-2018.)
Assertion
Ref Expression
intnexr ( A = V → ¬ A V)

Proof of Theorem intnexr
StepHypRef Expression
1 vprc 3879 . 2 ¬ V V
2 eleq1 2097 . 2 ( A = V → ( A V ↔ V V))
31, 2mtbiri 599 1 ( A = V → ¬ A V)
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4   = wceq 1242   ∈ wcel 1390  Vcvv 2551  ∩ cint 3606 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-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-13 1401  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019  ax-sep 3866 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-v 2553 This theorem is referenced by: (None)
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