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Theorem cvnref 23799
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 23798 . . 3  |-  ( ( A  e.  CH  /\  A  e.  CH )  ->  ( A  <oH  A  ->  -.  A  <oH  A ) )
21anidms 628 . 2  |-  ( A  e.  CH  ->  ( A  <oH  A  ->  -.  A  <oH  A ) )
32pm2.01d 164 1  |-  ( A  e.  CH  ->  -.  A  <oH  A )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    e. wcel 1726   class class class wbr 4215   CHcch 22437    <oH ccv 22472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-pss 3338  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4216  df-opab 4270  df-cv 23787
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