Theorem nvel 3863

Description: The universal class doesn't 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 3862	. 2 ⊢ ¬ V ∈ V
2		elex 2543	. 2 ⊢ (V ∈ A → V ∈ V)
3	1, 2	mto 575	1 ⊢ ¬ V ∈ A

Syntax hints:  ¬ wn 3   ∈ wcel 1374  Vcvv 2535

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 532  ax-in2 533  ax-5 1316  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-4 1381  ax-13 1385  ax-14 1386  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-ext 2004  ax-sep 3849

This theorem depends on definitions:  df-bi 110  df-tru 1231  df-fal 1234  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-v 2537

This theorem is referenced by: (None)