Theorem nvel 4797

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 4796	. 2 |- -. _V e. _V
2		elex 3212	. 2 |- ( _V e. A -> _V e. _V )
3	1, 2	mto 188	1 |- -. _V e. A

Syntax hints:   -. wn 3   e. wcel 1990   _Vcvv 3200

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-8 1992  ax-9 1999  ax-12 2047  ax-13 2246  ax-ext 2602  ax-sep 4781

This theorem depends on definitions:  df-bi 197  df-an 386  df-tru 1486  df-ex 1705  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-v 3202

This theorem is referenced by:  eliuniincex  39292  eliincex  39293  nvelim  41200