Theorem nvel 3880

Description: The universal class doesn't belong to any class. (Contributed by FL, 31-Dec-2006.)

Assertion

Ref	Expression
nvel	⊢ ¬ V ∈ A

Proof of Theorem nvel

Step	Hyp	Ref	Expression
1		vprc 3879	. 2 ⊢ ¬ V ∈ V
2		elex 2560	. 2 ⊢ (V ∈ A → V ∈ V)
3	1, 2	mto 587	1 ⊢ ¬ V ∈ A

Syntax hints:  ¬ wn 3   ∈ wcel 1390  Vcvv 2551

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-13 1401  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019  ax-sep 3866

This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-v 2553

This theorem is referenced by: (None)