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

Theorem bj-nvel 9890
 Description: nvel 3886 from bounded separation. (Contributed by BJ, 18-Nov-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-nvel ¬ V ∈ 𝐴

Proof of Theorem bj-nvel
StepHypRef Expression
1 bj-vprc 9889 . 2 ¬ V ∈ V
2 elex 2563 . 2 (V ∈ 𝐴 → V ∈ V)
31, 2mto 588 1 ¬ V ∈ 𝐴
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   ∈ wcel 1393  Vcvv 2554 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 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-4 1400  ax-13 1404  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-ext 2022  ax-bdn 9810  ax-bdel 9814  ax-bdsep 9877 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-v 2556 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator