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Theorem omlop 38713
Description: An orthomodular lattice is an orthoposet. (Contributed by NM, 6-Nov-2011.)
Assertion
Ref Expression
omlop (𝐾 ∈ OML → 𝐾 ∈ OP)

Proof of Theorem omlop
StepHypRef Expression
1 omlol 38712 . 2 (𝐾 ∈ OML → 𝐾 ∈ OL)
2 olop 38686 . 2 (𝐾 ∈ OL → 𝐾 ∈ OP)
31, 2syl 17 1 (𝐾 ∈ OML → 𝐾 ∈ OP)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2099  OPcops 38644  OLcol 38646  OMLcoml 38647
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-3an 1087  df-tru 1537  df-fal 1547  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-ral 3059  df-rab 3430  df-v 3473  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4324  df-if 4530  df-sn 4630  df-pr 4632  df-op 4636  df-uni 4909  df-br 5149  df-iota 6500  df-fv 6556  df-ov 7423  df-ol 38650  df-oml 38651
This theorem is referenced by:  omllaw2N  38716  omllaw4  38718  cmtcomlemN  38720  cmt2N  38722  cmt3N  38723  cmt4N  38724  cmtbr2N  38725  cmtbr3N  38726  cmtbr4N  38727  lecmtN  38728  omlfh1N  38730  omlfh3N  38731  omlspjN  38733  atlatmstc  38791
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