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Theorem cvlposN 34341
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 34340 . 2  |-  ( K  e.  CvLat  ->  K  e.  Lat )
2 latpos 15540 . 2  |-  ( K  e.  Lat  ->  K  e.  Poset )
31, 2syl 16 1  |-  ( K  e.  CvLat  ->  K  e.  Poset
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1767   Posetcpo 15430   Latclat 15535   CvLatclc 34279
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2819  df-rex 2820  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-uni 4246  df-br 4448  df-opab 4506  df-xp 5005  df-dm 5009  df-iota 5551  df-fv 5596  df-ov 6288  df-lat 15536  df-atl 34312  df-cvlat 34336
This theorem is referenced by: (None)
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