Theorem nvel 5286

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 5285	. 2 ⊢ ¬ V ∈ V
2		elex 3480	. 2 ⊢ (V ∈ 𝐴 → V ∈ V)
3	1, 2	mto 197	1 ⊢ ¬ V ∈ 𝐴

Syntax hints:  ¬ wn 3   ∈ wcel 2108  Vcvv 3459

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 2007  ax-8 2110  ax-9 2118  ax-ext 2707  ax-sep 5266

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2714  df-cleq 2727  df-clel 2809  df-v 3461

This theorem is referenced by:  curryset  36964  currysetlem3  36967  eliuniincex  45133  eliincex  45134  nvelim  47152