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Theorem cvlposN 32631
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 32630 . 2  |-  ( K  e.  CvLat  ->  K  e.  Lat )
2 latpos 16240 . 2  |-  ( K  e.  Lat  ->  K  e.  Poset )
31, 2syl 17 1  |-  ( K  e.  CvLat  ->  K  e.  Poset
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1867   Posetcpo 16129   Latclat 16235   CvLatclc 32569
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-ne 2618  df-ral 2778  df-rex 2779  df-rab 2782  df-v 3080  df-dif 3436  df-un 3438  df-in 3440  df-ss 3447  df-nul 3759  df-if 3907  df-sn 3994  df-pr 3996  df-op 4000  df-uni 4214  df-br 4418  df-opab 4476  df-xp 4851  df-dm 4855  df-iota 5556  df-fv 5600  df-ov 6299  df-lat 16236  df-atl 32602  df-cvlat 32626
This theorem is referenced by: (None)
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