Theorem nvel 4176

Description: The universal class does not 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 4175	. 2 |- -. _V e. _V
2		elex 2782	. 2 |- ( _V e. A -> _V e. _V )
3	1, 2	mto 663	1 |- -. _V e. A

Syntax hints:   -. wn 3   e. wcel 2175   _Vcvv 2771

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-5 1469  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-13 2177  ax-14 2178  ax-ext 2186  ax-sep 4161

This theorem depends on definitions:  df-bi 117  df-tru 1375  df-fal 1378  df-nf 1483  df-sb 1785  df-clab 2191  df-cleq 2197  df-clel 2200  df-v 2773

This theorem is referenced by: (None)