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Theorem cvlposN 29517
Description: An atomic lattice with the covering property is a poset. (Contributed by NM, 5-Nov-2012.) (New usage is discouraged.)
Assertion
Ref Expression
cvlposN  |-  ( K  e.  CvLat  ->  K  e.  Poset
)

Proof of Theorem cvlposN
StepHypRef Expression
1 cvllat 29516 . 2  |-  ( K  e.  CvLat  ->  K  e.  Lat )
2 latpos 14155 . 2  |-  ( K  e.  Lat  ->  K  e.  Poset )
31, 2syl 15 1  |-  ( K  e.  CvLat  ->  K  e.  Poset
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1684   Posetcpo 14074   Latclat 14151   CvLatclc 29455
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-iota 5219  df-fv 5263  df-ov 5861  df-lat 14152  df-atl 29488  df-cvlat 29512
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