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Theorem omlop 38615
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 38614 . 2 (𝐾 ∈ OML → 𝐾 ∈ OL)
2 olop 38588 . 2 (𝐾 ∈ OL → 𝐾 ∈ OP)
31, 2syl 17 1 (𝐾 ∈ OML → 𝐾 ∈ OP)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2098  OPcops 38546  OLcol 38548  OMLcoml 38549
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 2695
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 2702  df-cleq 2716  df-clel 2802  df-ral 3054  df-rab 3425  df-v 3468  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-nul 4316  df-if 4522  df-sn 4622  df-pr 4624  df-op 4628  df-uni 4901  df-br 5140  df-iota 6486  df-fv 6542  df-ov 7405  df-ol 38552  df-oml 38553
This theorem is referenced by:  omllaw2N  38618  omllaw4  38620  cmtcomlemN  38622  cmt2N  38624  cmt3N  38625  cmt4N  38626  cmtbr2N  38627  cmtbr3N  38628  cmtbr4N  38629  lecmtN  38630  omlfh1N  38632  omlfh3N  38633  omlspjN  38635  atlatmstc  38693
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