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Theorem omlop 29431
Description: An orthomodular lattice is an orthoposet. (Contributed by NM, 6-Nov-2011.)
Assertion
Ref Expression
omlop  |-  ( K  e.  OML  ->  K  e.  OP )

Proof of Theorem omlop
StepHypRef Expression
1 omlol 29430 . 2  |-  ( K  e.  OML  ->  K  e.  OL )
2 olop 29404 . 2  |-  ( K  e.  OL  ->  K  e.  OP )
31, 2syl 15 1  |-  ( K  e.  OML  ->  K  e.  OP )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1684   OPcops 29362   OLcol 29364   OMLcoml 29365
This theorem is referenced by:  omllaw2N  29434  omllaw4  29436  cmtcomlemN  29438  cmt2N  29440  cmt3N  29441  cmt4N  29442  cmtbr2N  29443  cmtbr3N  29444  cmtbr4N  29445  lecmtN  29446  omlfh1N  29448  omlfh3N  29449  omlspjN  29451  atlatmstc  29509
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-iota 5219  df-fv 5263  df-ov 5861  df-ol 29368  df-oml 29369
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