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Theorem omlop 30113
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 30112 . 2  |-  ( K  e.  OML  ->  K  e.  OL )
2 olop 30086 . 2  |-  ( K  e.  OL  ->  K  e.  OP )
31, 2syl 16 1  |-  ( K  e.  OML  ->  K  e.  OP )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1726   OPcops 30044   OLcol 30046   OMLcoml 30047
This theorem is referenced by:  omllaw2N  30116  omllaw4  30118  cmtcomlemN  30120  cmt2N  30122  cmt3N  30123  cmt4N  30124  cmtbr2N  30125  cmtbr3N  30126  cmtbr4N  30127  lecmtN  30128  omlfh1N  30130  omlfh3N  30131  omlspjN  30133  atlatmstc  30191
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-iota 5421  df-fv 5465  df-ov 6087  df-ol 30050  df-oml 30051
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