Theorem bj-vnex 13085

Description: vnex 4054 from bounded separation. (Contributed by BJ, 18-Nov-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-vnex	⊢ ¬ ∃𝑥 𝑥 = V

Proof of Theorem bj-vnex

Step	Hyp	Ref	Expression
1		bj-vprc 13083	. 2 ⊢ ¬ V ∈ V
2		isset 2687	. 2 ⊢ (V ∈ V ↔ ∃𝑥 𝑥 = V)
3	1, 2	mtbi 659	1 ⊢ ¬ ∃𝑥 𝑥 = V

Syntax hints:  ¬ wn 3   = wceq 1331  ∃wex 1468   ∈ wcel 1480  Vcvv 2681

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)