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Theorem hloml 29616
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 29615 . 2  |-  ( K  e.  HL  ->  ( K  e.  OML  /\  K  e.  CLat  /\  K  e.  CvLat
) )
21simp1d 967 1  |-  ( K  e.  HL  ->  K  e.  OML )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1710   CLatccla 14312   OMLcoml 29434   CvLatclc 29524   HLchlt 29609
This theorem is referenced by:  hlol  29620  hlomcmat  29623  poml4N  30211  doca2N  31385  djajN  31396  dihoml4c  31635
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-ral 2624  df-rex 2625  df-rab 2628  df-v 2866  df-dif 3231  df-un 3233  df-in 3235  df-ss 3242  df-nul 3532  df-if 3642  df-sn 3722  df-pr 3723  df-op 3725  df-uni 3909  df-br 4105  df-iota 5301  df-fv 5345  df-ov 5948  df-hlat 29610
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