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Theorem omlop 34668
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 34667 . 2  |-  ( K  e.  OML  ->  K  e.  OL )
2 olop 34641 . 2  |-  ( K  e.  OL  ->  K  e.  OP )
31, 2syl 16 1  |-  ( K  e.  OML  ->  K  e.  OP )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1802   OPcops 34599   OLcol 34601   OMLcoml 34602
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1603  ax-4 1616  ax-5 1689  ax-6 1732  ax-7 1774  ax-10 1821  ax-11 1826  ax-12 1838  ax-13 1983  ax-ext 2419
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 974  df-tru 1384  df-ex 1598  df-nf 1602  df-sb 1725  df-clab 2427  df-cleq 2433  df-clel 2436  df-nfc 2591  df-ral 2796  df-rex 2797  df-rab 2800  df-v 3095  df-dif 3461  df-un 3463  df-in 3465  df-ss 3472  df-nul 3768  df-if 3923  df-sn 4011  df-pr 4013  df-op 4017  df-uni 4231  df-br 4434  df-iota 5537  df-fv 5582  df-ov 6280  df-ol 34605  df-oml 34606
This theorem is referenced by:  omllaw2N  34671  omllaw4  34673  cmtcomlemN  34675  cmt2N  34677  cmt3N  34678  cmt4N  34679  cmtbr2N  34680  cmtbr3N  34681  cmtbr4N  34682  lecmtN  34683  omlfh1N  34685  omlfh3N  34686  omlspjN  34688  atlatmstc  34746
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