Theorem nvel 4222

Description: The universal class does not 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 4221	. 2 ⊢ ¬ V ∈ V
2		elex 2814	. 2 ⊢ (V ∈ 𝐴 → V ∈ V)
3	1, 2	mto 668	1 ⊢ ¬ V ∈ 𝐴

Syntax hints:  ¬ wn 3   ∈ wcel 2202  Vcvv 2802

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 619  ax-in2 620  ax-5 1495  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-13 2204  ax-14 2205  ax-ext 2213  ax-sep 4207

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-fal 1403  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-v 2804

This theorem is referenced by: (None)