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Theorem cvnref 28999
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 28998 . . 3 ((𝐴C𝐴C ) → (𝐴 𝐴 → ¬ 𝐴 𝐴))
21anidms 676 . 2 (𝐴C → (𝐴 𝐴 → ¬ 𝐴 𝐴))
32pm2.01d 181 1 (𝐴C → ¬ 𝐴 𝐴)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wcel 1987   class class class wbr 4613   C cch 27635   ccv 27670
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-sep 4741  ax-nul 4749  ax-pr 4867
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-eu 2473  df-mo 2474  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-ne 2791  df-rex 2913  df-rab 2916  df-v 3188  df-dif 3558  df-un 3560  df-in 3562  df-ss 3569  df-pss 3571  df-nul 3892  df-if 4059  df-sn 4149  df-pr 4151  df-op 4155  df-br 4614  df-opab 4674  df-cv 28987
This theorem is referenced by: (None)
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