Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bj-intnexr GIF version

Theorem bj-intnexr 11683
Description: intnexr 3985 from bounded separation. (Contributed by BJ, 18-Nov-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-intnexr ( 𝐴 = V → ¬ 𝐴 ∈ V)

Proof of Theorem bj-intnexr
StepHypRef Expression
1 bj-vprc 11670 . 2 ¬ V ∈ V
2 eleq1 2150 . 2 ( 𝐴 = V → ( 𝐴 ∈ V ↔ V ∈ V))
31, 2mtbiri 635 1 ( 𝐴 = V → ¬ 𝐴 ∈ V)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1289  wcel 1438  Vcvv 2619   cint 3686
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-4 1445  ax-13 1449  ax-14 1450  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-ext 2070  ax-bdn 11591  ax-bdel 11595  ax-bdsep 11658
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-fal 1295  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-v 2621
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator