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Theorem cvnref 32114
Description: The covers relation is not reflexive. (Contributed by NM, 26-Jun-2004.) (New usage is discouraged.)
Assertion
Ref Expression
cvnref (𝐴C → ¬ 𝐴 𝐴)

Proof of Theorem cvnref
StepHypRef Expression
1 cvnsym 32113 . . 3 ((𝐴C𝐴C ) → (𝐴 𝐴 → ¬ 𝐴 𝐴))
21anidms 566 . 2 (𝐴C → (𝐴 𝐴 → ¬ 𝐴 𝐴))
32pm2.01d 189 1 (𝐴C → ¬ 𝐴 𝐴)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wcel 2099   class class class wbr 5148   C cch 30752   ccv 30787
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699  ax-sep 5299  ax-nul 5306  ax-pr 5429
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-3an 1087  df-tru 1537  df-fal 1547  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-ne 2938  df-rex 3068  df-rab 3430  df-v 3473  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-pss 3966  df-nul 4324  df-if 4530  df-sn 4630  df-pr 4632  df-op 4636  df-br 5149  df-opab 5211  df-cv 32102
This theorem is referenced by: (None)
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