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Theorem prcnel 3249
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 ∈ V → ¬ 𝐴𝑉)

Proof of Theorem prcnel
StepHypRef Expression
1 elex 3243 . 2 (𝐴𝑉𝐴 ∈ V)
21con3i 150 1 𝐴 ∈ V → ¬ 𝐴𝑉)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wcel 2030  Vcvv 3231
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-12 2087  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-an 385  df-tru 1526  df-ex 1745  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-v 3233
This theorem is referenced by:  fundmge2nop0  13312  fun2dmnop0  13314  vtxval  25923  iedgval  25924  eliin2f  39601  afvprc  41545
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