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Theorem prcnel 3434
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 3428 . 2 (𝐴𝑉𝐴 ∈ V)
21con3i 152 1 𝐴 ∈ V → ¬ 𝐴𝑉)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wcel 2166  Vcvv 3413
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-9 2175  ax-12 2222  ax-ext 2802
This theorem depends on definitions:  df-bi 199  df-an 387  df-tru 1662  df-ex 1881  df-sb 2070  df-clab 2811  df-cleq 2817  df-clel 2820  df-v 3415
This theorem is referenced by:  fundmge2nop0  13562  fun2dmnop0  13564  vtxval  26297  iedgval  26298  eliin2f  40101  dfatprc  42031  afvprc  42045  afv2prc  42127
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