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Theorem omllat 35016
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 35014 . 2 (𝐾 ∈ OML → 𝐾 ∈ OL)
2 ollat 34987 . 2 (𝐾 ∈ OL → 𝐾 ∈ Lat)
31, 2syl 17 1 (𝐾 ∈ OML → 𝐾 ∈ Lat)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2155  Latclat 17244  OLcol 34948  OMLcoml 34949
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001  ax-6 2067  ax-7 2103  ax-9 2164  ax-10 2184  ax-11 2200  ax-12 2213  ax-13 2419  ax-ext 2781
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 866  df-3an 1102  df-tru 1641  df-ex 1860  df-nf 1864  df-sb 2060  df-clab 2789  df-cleq 2795  df-clel 2798  df-nfc 2933  df-ral 3097  df-rex 3098  df-rab 3101  df-v 3389  df-dif 3766  df-un 3768  df-in 3770  df-ss 3777  df-nul 4111  df-if 4274  df-sn 4365  df-pr 4367  df-op 4371  df-uni 4624  df-br 4838  df-iota 6058  df-fv 6103  df-ov 6871  df-ol 34952  df-oml 34953
This theorem is referenced by:  omllaw2N  35018  omllaw4  35020  omllaw5N  35021  cmtcomlemN  35022  cmt2N  35024  cmtbr2N  35027  cmtbr3N  35028  cmtbr4N  35029  lecmtN  35030  cmtidN  35031  omlfh1N  35032  omlfh3N  35033  omlmod1i2N  35034  omlspjN  35035
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