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Theorem hloml 29840
Description: A Hilbert lattice is orthomodular. (Contributed by NM, 20-Oct-2011.)
Assertion
Ref Expression
hloml  |-  ( K  e.  HL  ->  K  e.  OML )

Proof of Theorem hloml
StepHypRef Expression
1 hlomcmcv 29839 . 2  |-  ( K  e.  HL  ->  ( K  e.  OML  /\  K  e.  CLat  /\  K  e.  CvLat
) )
21simp1d 969 1  |-  ( K  e.  HL  ->  K  e.  OML )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1721   CLatccla 14491   OMLcoml 29658   CvLatclc 29748   HLchlt 29833
This theorem is referenced by:  hlol  29844  hlomcmat  29847  poml4N  30435  doca2N  31609  djajN  31620  dihoml4c  31859
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ral 2671  df-rex 2672  df-rab 2675  df-v 2918  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-nul 3589  df-if 3700  df-sn 3780  df-pr 3781  df-op 3783  df-uni 3976  df-br 4173  df-iota 5377  df-fv 5421  df-ov 6043  df-hlat 29834
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