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Theorem omllat 29977
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 29975 . 2  |-  ( K  e.  OML  ->  K  e.  OL )
2 ollat 29948 . 2  |-  ( K  e.  OL  ->  K  e.  Lat )
31, 2syl 16 1  |-  ( K  e.  OML  ->  K  e.  Lat )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1725   Latclat 14466   OLcol 29909   OMLcoml 29910
This theorem is referenced by:  omllaw2N  29979  omllaw4  29981  omllaw5N  29982  cmtcomlemN  29983  cmt2N  29985  cmtbr2N  29988  cmtbr3N  29989  cmtbr4N  29990  lecmtN  29991  cmtidN  29992  omlfh1N  29993  omlfh3N  29994  omlmod1i2N  29995  omlspjN  29996
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-ov 6076  df-ol 29913  df-oml 29914
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