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Theorem cvlposN 36581
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 36580 . 2 (𝐾 ∈ CvLat → 𝐾 ∈ Lat)
2 latpos 17651 . 2 (𝐾 ∈ Lat → 𝐾 ∈ Poset)
31, 2syl 17 1 (𝐾 ∈ CvLat → 𝐾 ∈ Poset)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2114  Posetcpo 17541  Latclat 17646  CvLatclc 36519
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2178  ax-ext 2794
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2801  df-cleq 2815  df-clel 2894  df-nfc 2962  df-ne 3012  df-ral 3135  df-rex 3136  df-rab 3139  df-v 3471  df-un 3913  df-in 3915  df-ss 3925  df-sn 4540  df-pr 4542  df-op 4546  df-uni 4814  df-br 5043  df-opab 5105  df-xp 5538  df-dm 5542  df-iota 6293  df-fv 6342  df-ov 7143  df-lat 17647  df-atl 36552  df-cvlat 36576
This theorem is referenced by: (None)
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