Theorem nvel 2714

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		nvelv 2713	. 2 |- -. V e. V
2		elisset 1817	. 2 |- (V e. A -> V e. V)
3	1, 2	mto 106	1 |- -. V e. A

Syntax hints:  -. wn 2   e. wcel 958  Vcvv 1811

This theorem is referenced by:  fiiu 10453  fiiuOLD 10454  fiiu2 10488  fiiu2OLD 10489

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-8 964  ax-12 968  ax-13 969  ax-14 970  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-ext 1459  ax-sep 2703

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812

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