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Theorem bj-intnexr 13096
 Description: intnexr 4071 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 13083 . 2 ¬ V ∈ V
2 eleq1 2200 . 2 ( 𝐴 = V → ( 𝐴 ∈ V ↔ V ∈ V))
31, 2mtbiri 664 1 ( 𝐴 = V → ¬ 𝐴 ∈ V)
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4   = wceq 1331   ∈ wcel 1480  Vcvv 2681  ∩ cint 3766 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-13 1491  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-ext 2119  ax-bdn 13004  ax-bdel 13008  ax-bdsep 13071 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-v 2683 This theorem is referenced by: (None)
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