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Theorem cvlposN 39306
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 ∈ CvLat → 𝐾 ∈ Poset)

Proof of Theorem cvlposN
StepHypRef Expression
1 cvllat 39305 . 2 (𝐾 ∈ CvLat → 𝐾 ∈ Lat)
2 latpos 18479 . 2 (𝐾 ∈ Lat → 𝐾 ∈ Poset)
31, 2syl 17 1 (𝐾 ∈ CvLat → 𝐾 ∈ Poset)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2108  Posetcpo 18349  Latclat 18472  CvLatclc 39244
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2714  df-cleq 2728  df-clel 2815  df-ne 2940  df-ral 3061  df-rex 3070  df-rab 3436  df-v 3481  df-dif 3953  df-un 3955  df-ss 3967  df-nul 4333  df-if 4525  df-sn 4625  df-pr 4627  df-op 4631  df-uni 4906  df-br 5142  df-opab 5204  df-xp 5689  df-dm 5693  df-iota 6512  df-fv 6567  df-ov 7432  df-lat 18473  df-atl 39277  df-cvlat 39301
This theorem is referenced by: (None)
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