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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
StepHypRef Expression
1 elex 3040 . 2  |-  ( A  e.  V  ->  A  e.  _V )
21con3i 142 1  |-  ( -.  A  e.  _V  ->  -.  A  e.  V )
Colors of variables: wff setvar class
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
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