Theorem nvel 5316

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 5315	. 2 ⊢ ¬ V ∈ V
2		elex 3492	. 2 ⊢ (V ∈ 𝐴 → V ∈ V)
3	1, 2	mto 196	1 ⊢ ¬ V ∈ 𝐴

Syntax hints:  ¬ wn 3   ∈ wcel 2106  Vcvv 3474

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703  ax-sep 5299

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-v 3476

This theorem is referenced by:  curryset  35822  currysetlem3  35825  eliuniincex  43788  eliincex  43789  nvelim  45821