Theorem bj-vnex 16493

Description: vnex 4220 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 16491	. 2 ⊢ ¬ V ∈ V
2		isset 2809	. 2 ⊢ (V ∈ V ↔ ∃𝑥 𝑥 = V)
3	1, 2	mtbi 676	1 ⊢ ¬ ∃𝑥 𝑥 = V

Syntax hints:  ¬ wn 3   = wceq 1397  ∃wex 1540   ∈ wcel 2202  Vcvv 2802

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 619  ax-in2 620  ax-5 1495  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-13 2204  ax-14 2205  ax-ext 2213  ax-bdn 16412  ax-bdel 16416  ax-bdsep 16479

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-fal 1403  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-v 2804

This theorem is referenced by: (None)