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Theorem cvnref 22979
Description: The covers relation is not reflexive. (Contributed by NM, 26-Jun-2004.) (New usage is discouraged.)
Assertion
Ref Expression
cvnref  |-  ( A  e.  CH  ->  -.  A  <oH  A )

Proof of Theorem cvnref
StepHypRef Expression
1 cvnsym 22978 . . 3  |-  ( ( A  e.  CH  /\  A  e.  CH )  ->  ( A  <oH  A  ->  -.  A  <oH  A ) )
21anidms 626 . 2  |-  ( A  e.  CH  ->  ( A  <oH  A  ->  -.  A  <oH  A ) )
32pm2.01d 161 1  |-  ( A  e.  CH  ->  -.  A  <oH  A )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    e. wcel 1710   class class class wbr 4102   CHcch 21617    <oH ccv 21652
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-14 1714  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339  ax-sep 4220  ax-nul 4228  ax-pr 4293
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2213  df-mo 2214  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-ne 2523  df-rex 2625  df-rab 2628  df-v 2866  df-dif 3231  df-un 3233  df-in 3235  df-ss 3242  df-pss 3244  df-nul 3532  df-if 3642  df-sn 3722  df-pr 3723  df-op 3725  df-br 4103  df-opab 4157  df-cv 22967
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