Theorem nvel 5213

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 5212	. 2 ⊢ ¬ V ∈ V
2		elex 3513	. 2 ⊢ (V ∈ 𝐴 → V ∈ V)
3	1, 2	mto 199	1 ⊢ ¬ V ∈ 𝐴

Syntax hints:  ¬ wn 3   ∈ wcel 2110  Vcvv 3495

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-8 2112  ax-9 2120  ax-ext 2793  ax-sep 5196

This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1777  df-sb 2066  df-clab 2800  df-cleq 2814  df-clel 2893  df-v 3497

This theorem is referenced by:  curryset  34252  currysetlem3  34255  eliuniincex  41368  eliincex  41369  nvelim  43315