Theorem prcnel 3046

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 3040	. 2 |- ( A e. V -> A e. _V )
2	1	con3i 142	1 |- ( -. A e. _V -> -. A e. V )

Syntax hints:   -. wn 3   -> wi 4   e. wcel 1904   _Vcvv 3031

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-12 1950  ax-ext 2451

This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-v 3033

This theorem is referenced by:  nelsn  3992  fun2dmnop  39173