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Theorem cvlposN 29569
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 29568 . 2  |-  ( K  e.  CvLat  ->  K  e.  Lat )
2 latpos 14248 . 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 1710   Posetcpo 14167   Latclat 14244   CvLatclc 29507
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-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339
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-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-ne 2523  df-ral 2624  df-rex 2625  df-rab 2628  df-v 2866  df-dif 3231  df-un 3233  df-in 3235  df-ss 3242  df-nul 3532  df-if 3642  df-sn 3722  df-pr 3723  df-op 3725  df-uni 3907  df-br 4103  df-iota 5298  df-fv 5342  df-ov 5945  df-lat 14245  df-atl 29540  df-cvlat 29564
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