HSE Home Hilbert Space Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  HSE Home  >  Th. List  >  cvnref Structured version   Visualization version   GIF version

Theorem cvnref 29849
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 29848 . . 3 ((𝐴C𝐴C ) → (𝐴 𝐴 → ¬ 𝐴 𝐴))
21anidms 559 . 2 (𝐴C → (𝐴 𝐴 → ¬ 𝐴 𝐴))
32pm2.01d 182 1 (𝐴C → ¬ 𝐴 𝐴)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wcel 2050   class class class wbr 4929   C cch 28485   ccv 28520
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-8 2052  ax-9 2059  ax-10 2079  ax-11 2093  ax-12 2106  ax-13 2301  ax-ext 2750  ax-sep 5060  ax-nul 5067  ax-pr 5186
This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-3an 1070  df-tru 1510  df-ex 1743  df-nf 1747  df-sb 2016  df-mo 2547  df-eu 2584  df-clab 2759  df-cleq 2771  df-clel 2846  df-nfc 2918  df-ne 2968  df-rex 3094  df-rab 3097  df-v 3417  df-dif 3832  df-un 3834  df-in 3836  df-ss 3843  df-pss 3845  df-nul 4179  df-if 4351  df-sn 4442  df-pr 4444  df-op 4448  df-br 4930  df-opab 4992  df-cv 29837
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator