Theorem bj-vnex 16033

Description: vnex 4191 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 16031	. 2 ⊢ ¬ V ∈ V
2		isset 2783	. 2 ⊢ (V ∈ V ↔ ∃𝑥 𝑥 = V)
3	1, 2	mtbi 672	1 ⊢ ¬ ∃𝑥 𝑥 = V

Syntax hints:  ¬ wn 3   = wceq 1373  ∃wex 1516   ∈ wcel 2178  Vcvv 2776

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-5 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-13 2180  ax-14 2181  ax-ext 2189  ax-bdn 15952  ax-bdel 15956  ax-bdsep 16019

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-fal 1379  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-v 2778

This theorem is referenced by: (None)