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Theorem omllat 35364
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 35362 . 2  |-  ( K  e.  OML  ->  K  e.  OL )
2 ollat 35335 . 2  |-  ( K  e.  OL  ->  K  e.  Lat )
31, 2syl 16 1  |-  ( K  e.  OML  ->  K  e.  Lat )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1823   Latclat 15874   OLcol 35296   OMLcoml 35297
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 973  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ral 2809  df-rex 2810  df-rab 2813  df-v 3108  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3784  df-if 3930  df-sn 4017  df-pr 4019  df-op 4023  df-uni 4236  df-br 4440  df-iota 5534  df-fv 5578  df-ov 6273  df-ol 35300  df-oml 35301
This theorem is referenced by:  omllaw2N  35366  omllaw4  35368  omllaw5N  35369  cmtcomlemN  35370  cmt2N  35372  cmtbr2N  35375  cmtbr3N  35376  cmtbr4N  35377  lecmtN  35378  cmtidN  35379  omlfh1N  35380  omlfh3N  35381  omlmod1i2N  35382  omlspjN  35383
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