Theorem nvel 3450

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 3449	. 2 |- -. _V e. _V
2		elisset 2299	. 2 |- (_V e. A -> _V e. _V)
3	1, 2	mto 121	1 |- -. _V e. A

Syntax hints:  -. wn 2   e. wcel 1300  _Vcvv 2292

This theorem is referenced by:  fiiu2 10220  fiiu 14344

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1305  ax-8 1306  ax-12 1310  ax-13 1311  ax-14 1312  ax-17 1317  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-ext 1865  ax-sep 3438

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327  df-sb 1536  df-clab 1872  df-cleq 1877  df-clel 1880  df-v 2294

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