Users' Mathboxes Mathbox for Norm Megill < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  omlop Structured version   Visualization version   GIF version

Theorem omlop 35023
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 35022 . 2 (𝐾 ∈ OML → 𝐾 ∈ OL)
2 olop 34996 . 2 (𝐾 ∈ OL → 𝐾 ∈ OP)
31, 2syl 17 1 (𝐾 ∈ OML → 𝐾 ∈ OP)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2157  OPcops 34954  OLcol 34956  OMLcoml 34957
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 2069  ax-7 2105  ax-9 2166  ax-10 2186  ax-11 2202  ax-12 2215  ax-13 2422  ax-ext 2791
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 2062  df-clab 2800  df-cleq 2806  df-clel 2809  df-nfc 2944  df-ral 3108  df-rex 3109  df-rab 3112  df-v 3400  df-dif 3779  df-un 3781  df-in 3783  df-ss 3790  df-nul 4124  df-if 4287  df-sn 4378  df-pr 4380  df-op 4384  df-uni 4638  df-br 4852  df-iota 6067  df-fv 6112  df-ov 6880  df-ol 34960  df-oml 34961
This theorem is referenced by:  omllaw2N  35026  omllaw4  35028  cmtcomlemN  35030  cmt2N  35032  cmt3N  35033  cmt4N  35034  cmtbr2N  35035  cmtbr3N  35036  cmtbr4N  35037  lecmtN  35038  omlfh1N  35040  omlfh3N  35041  omlspjN  35043  atlatmstc  35101
  Copyright terms: Public domain W3C validator