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Theorem prcnel 3496
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 3491 . 2 (𝐴𝑉𝐴 ∈ V)
21con3i 154 1 𝐴 ∈ V → ¬ 𝐴𝑉)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wcel 2104  Vcvv 3472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1911  ax-6 1969  ax-7 2009  ax-8 2106  ax-9 2114  ax-ext 2701
This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1542  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2722  df-clel 2808  df-v 3474
This theorem is referenced by:  suppco  8193  fundmge2nop0  14457  fun2dmnop0  14459  vtxval  28527  iedgval  28528  fmlafvel  34674  isinf2  36589  eliin2f  44094  dfatprc  46136  afvprc  46150  afv2prc  46232
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