Theorem vnex 2720

Description: The universal class does not exist.

Assertion

Ref	Expression
vnex	⊢ ¬ ∃x x = V

Proof of Theorem vnex

Step	Hyp	Ref	Expression
1		nvelv 2718	. 2 ⊢ ¬ V ∈ V
2		isset 1817	. 2 ⊢ (V ∈ V ↔ ∃x x = V)
3	1, 2	mtbi 191	1 ⊢ ¬ ∃x x = V

Syntax hints:  ¬ wn 2   = wceq 958   ∈ wcel 960  ∃wex 982  Vcvv 1814

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 965  ax-8 966  ax-12 970  ax-13 971  ax-14 972  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-ext 1462  ax-sep 2708

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-v 1815

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