Theorem nvel 3936

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 3935	. 2 |- -. _V e. _V
2		elex 2621	. 2 |- ( _V e. A -> _V e. _V )
3	1, 2	mto 621	1 |- -. _V e. A

Syntax hints:   -. wn 3   e. wcel 1434   _Vcvv 2612

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 577  ax-in2 578  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-4 1441  ax-13 1445  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-ext 2065  ax-sep 3922

This theorem depends on definitions:  df-bi 115  df-tru 1288  df-fal 1291  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-v 2614

This theorem is referenced by: (None)