Theorem nvel 5310

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 5309	. 2 ⊢ ¬ V ∈ V
2		elex 3488	. 2 ⊢ (V ∈ 𝐴 → V ∈ V)
3	1, 2	mto 196	1 ⊢ ¬ V ∈ 𝐴

Syntax hints:  ¬ wn 3   ∈ wcel 2099  Vcvv 3469

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2698  ax-sep 5293

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2705  df-cleq 2719  df-clel 2805  df-v 3471

This theorem is referenced by:  curryset  36415  currysetlem3  36418  eliuniincex  44447  eliincex  44448  nvelim  46475