Theorem nvel 5256

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 5255	. 2 ⊢ ¬ V ∈ V
2		elex 3458	. 2 ⊢ (V ∈ 𝐴 → V ∈ V)
3	1, 2	mto 197	1 ⊢ ¬ V ∈ 𝐴

Syntax hints:  ¬ wn 3   ∈ wcel 2113  Vcvv 3437

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2705  ax-sep 5236

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2712  df-cleq 2725  df-clel 2808  df-v 3439

This theorem is referenced by:  onvf1odlem1  35168  curryset  37011  currysetlem3  37014  eliuniincex  45230  eliincex  45231  nvelim  47247