Theorem prcnel 3218

Description: A proper class doesn't belong to any class. (Contributed by Glauco Siliprandi, 17-Aug-2020.) (Proof shortened by AV, 14-Nov-2020.)

Assertion

Ref	Expression
prcnel	|- ( -. A e. _V -> -. A e. V )

Proof of Theorem prcnel

Step	Hyp	Ref	Expression
1		elex 3212	. 2 |- ( A e. V -> A e. _V )
2	1	con3i 150	1 |- ( -. A e. _V -> -. A e. V )

Syntax hints:   -. wn 3   -> wi 4   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-9 1999  ax-12 2047  ax-ext 2602

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:  nelsnOLD  4213  fundmge2nop0  13274  fun2dmnop0  13276  vtxval  25878  iedgval  25879  eliin2f  39287  afvprc  41224