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Theorem omllat 36852
 Description: An orthomodular lattice is a lattice. (Contributed by NM, 6-Nov-2011.)
Assertion
Ref Expression
omllat (𝐾 ∈ OML → 𝐾 ∈ Lat)

Proof of Theorem omllat
StepHypRef Expression
1 omlol 36850 . 2 (𝐾 ∈ OML → 𝐾 ∈ OL)
2 ollat 36823 . 2 (𝐾 ∈ OL → 𝐾 ∈ Lat)
31, 2syl 17 1 (𝐾 ∈ OML → 𝐾 ∈ Lat)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 2111  Latclat 17734  OLcol 36784  OMLcoml 36785 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 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2729 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 2736  df-cleq 2750  df-clel 2830  df-nfc 2901  df-ral 3075  df-rab 3079  df-v 3411  df-un 3865  df-in 3867  df-ss 3877  df-sn 4526  df-pr 4528  df-op 4532  df-uni 4802  df-br 5037  df-iota 6299  df-fv 6348  df-ov 7159  df-ol 36788  df-oml 36789 This theorem is referenced by:  omllaw2N  36854  omllaw4  36856  omllaw5N  36857  cmtcomlemN  36858  cmt2N  36860  cmtbr2N  36863  cmtbr3N  36864  cmtbr4N  36865  lecmtN  36866  cmtidN  36867  omlfh1N  36868  omlfh3N  36869  omlmod1i2N  36870  omlspjN  36871
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