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Theorem omllat 36245
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 36243 . 2 (𝐾 ∈ OML → 𝐾 ∈ OL)
2 ollat 36216 . 2 (𝐾 ∈ OL → 𝐾 ∈ Lat)
31, 2syl 17 1 (𝐾 ∈ OML → 𝐾 ∈ Lat)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2107  Latclat 17645  OLcol 36177  OMLcoml 36178
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-ext 2798
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-3an 1083  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-clab 2805  df-cleq 2819  df-clel 2898  df-nfc 2968  df-ral 3148  df-rex 3149  df-rab 3152  df-v 3502  df-dif 3943  df-un 3945  df-in 3947  df-ss 3956  df-nul 4296  df-if 4471  df-sn 4565  df-pr 4567  df-op 4571  df-uni 4838  df-br 5064  df-iota 6312  df-fv 6360  df-ov 7151  df-ol 36181  df-oml 36182
This theorem is referenced by:  omllaw2N  36247  omllaw4  36249  omllaw5N  36250  cmtcomlemN  36251  cmt2N  36253  cmtbr2N  36256  cmtbr3N  36257  cmtbr4N  36258  lecmtN  36259  cmtidN  36260  omlfh1N  36261  omlfh3N  36262  omlmod1i2N  36263  omlspjN  36264
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