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Theorem omlop 33225
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 33224 . 2  |-  ( K  e.  OML  ->  K  e.  OL )
2 olop 33198 . 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 1758   OPcops 33156   OLcol 33158   OMLcoml 33159
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ral 2804  df-rex 2805  df-rab 2808  df-v 3080  df-dif 3440  df-un 3442  df-in 3444  df-ss 3451  df-nul 3747  df-if 3901  df-sn 3987  df-pr 3989  df-op 3993  df-uni 4201  df-br 4402  df-iota 5490  df-fv 5535  df-ov 6204  df-ol 33162  df-oml 33163
This theorem is referenced by:  omllaw2N  33228  omllaw4  33230  cmtcomlemN  33232  cmt2N  33234  cmt3N  33235  cmt4N  33236  cmtbr2N  33237  cmtbr3N  33238  cmtbr4N  33239  lecmtN  33240  omlfh1N  33242  omlfh3N  33243  omlspjN  33245  atlatmstc  33303
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