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Theorem omllat 38623
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 38621 . 2 (𝐾 ∈ OML → 𝐾 ∈ OL)
2 ollat 38594 . 2 (𝐾 ∈ OL → 𝐾 ∈ Lat)
31, 2syl 17 1 (𝐾 ∈ OML → 𝐾 ∈ Lat)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2098  Latclat 18394  OLcol 38555  OMLcoml 38556
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 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-ral 3056  df-rab 3427  df-v 3470  df-dif 3946  df-un 3948  df-in 3950  df-ss 3960  df-nul 4318  df-if 4524  df-sn 4624  df-pr 4626  df-op 4630  df-uni 4903  df-br 5142  df-iota 6488  df-fv 6544  df-ov 7407  df-ol 38559  df-oml 38560
This theorem is referenced by:  omllaw2N  38625  omllaw4  38627  omllaw5N  38628  cmtcomlemN  38629  cmt2N  38631  cmtbr2N  38634  cmtbr3N  38635  cmtbr4N  38636  lecmtN  38637  cmtidN  38638  omlfh1N  38639  omlfh3N  38640  omlmod1i2N  38641  omlspjN  38642
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