Theorem nvel 4830

Description: The universal class doesn't belong to any class. (Contributed by FL, 31-Dec-2006.)

Assertion

Ref	Expression
nvel	⊢ ¬ V ∈ 𝐴

Proof of Theorem nvel

Step	Hyp	Ref	Expression
1		vprc 4829	. 2 ⊢ ¬ V ∈ V
2		elex 3243	. 2 ⊢ (V ∈ 𝐴 → V ∈ V)
3	1, 2	mto 188	1 ⊢ ¬ V ∈ 𝐴

Syntax hints:  ¬ wn 3   ∈ wcel 2030  Vcvv 3231

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-8 2032  ax-9 2039  ax-12 2087  ax-13 2282  ax-ext 2631  ax-sep 4814

This theorem depends on definitions:  df-bi 197  df-an 385  df-tru 1526  df-ex 1745  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-v 3233

This theorem is referenced by:  eliuniincex  39606  eliincex  39607  nvelim  41521