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Theorem omllat 30054
Description: An orthomodular lattice is a lattice. (Contributed by NM, 6-Nov-2011.)
Assertion
Ref Expression
omllat  |-  ( K  e.  OML  ->  K  e.  Lat )

Proof of Theorem omllat
StepHypRef Expression
1 omlol 30052 . 2  |-  ( K  e.  OML  ->  K  e.  OL )
2 ollat 30025 . 2  |-  ( K  e.  OL  ->  K  e.  Lat )
31, 2syl 15 1  |-  ( K  e.  OML  ->  K  e.  Lat )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1696   Latclat 14167   OLcol 29986   OMLcoml 29987
This theorem is referenced by:  omllaw2N  30056  omllaw4  30058  omllaw5N  30059  cmtcomlemN  30060  cmt2N  30062  cmtbr2N  30065  cmtbr3N  30066  cmtbr4N  30067  lecmtN  30068  cmtidN  30069  omlfh1N  30070  omlfh3N  30071  omlmod1i2N  30072  omlspjN  30073
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-iota 5235  df-fv 5279  df-ov 5877  df-ol 29990  df-oml 29991
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