Theorem nvel 3910

Description: The universal class doesn't belong to any class. (Contributed by FL, 31-Dec-2006.)

Assertion

Ref	Expression
nvel	|- -. _V e. A

Proof of Theorem nvel

Step	Hyp	Ref	Expression
1		vprc 3909	. 2 |- -. _V e. _V
2		elex 2610	. 2 |- ( _V e. A -> _V e. _V )
3	1, 2	mto 620	1 |- -. _V e. A

Syntax hints:   -. wn 3   e. wcel 1433   _Vcvv 2601

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-4 1440  ax-13 1444  ax-14 1445  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-ext 2063  ax-sep 3896

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-fal 1290  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-v 2603

This theorem is referenced by: (None)