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Theorem cvnref 30077
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 30076 . . 3 ((𝐴C𝐴C ) → (𝐴 𝐴 → ¬ 𝐴 𝐴))
21anidms 570 . 2 (𝐴C → (𝐴 𝐴 → ¬ 𝐴 𝐴))
32pm2.01d 193 1 (𝐴C → ¬ 𝐴 𝐴)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wcel 2115   class class class wbr 5052   C cch 28715   ccv 28750
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796  ax-sep 5189  ax-nul 5196  ax-pr 5317
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-mo 2624  df-eu 2655  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-ne 3015  df-rex 3139  df-v 3482  df-dif 3922  df-un 3924  df-in 3926  df-ss 3936  df-pss 3938  df-nul 4277  df-if 4451  df-sn 4551  df-pr 4553  df-op 4557  df-br 5053  df-opab 5115  df-cv 30065
This theorem is referenced by: (None)
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