Theorem nvel 5291

Description: The universal class does not 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 5290	. 2 ⊢ ¬ V ∈ V
2		elex 3485	. 2 ⊢ (V ∈ 𝐴 → V ∈ V)
3	1, 2	mto 197	1 ⊢ ¬ V ∈ 𝐴

Syntax hints:  ¬ wn 3   ∈ wcel 2109  Vcvv 3464

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2708  ax-sep 5271

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2715  df-cleq 2728  df-clel 2810  df-v 3466

This theorem is referenced by:  curryset  36969  currysetlem3  36972  eliuniincex  45113  eliincex  45114  nvelim  47132