Users' Mathboxes Mathbox for Norm Megill < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  hloml Structured version   Unicode version

Theorem hloml 33310
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 33309 . 2  |-  ( K  e.  HL  ->  ( K  e.  OML  /\  K  e.  CLat  /\  K  e.  CvLat
) )
21simp1d 1000 1  |-  ( K  e.  HL  ->  K  e.  OML )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1758   CLatccla 15381   OMLcoml 33128   CvLatclc 33218   HLchlt 33303
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-ral 2800  df-rex 2801  df-rab 2804  df-v 3072  df-dif 3431  df-un 3433  df-in 3435  df-ss 3442  df-nul 3738  df-if 3892  df-sn 3978  df-pr 3980  df-op 3984  df-uni 4192  df-br 4393  df-iota 5481  df-fv 5526  df-ov 6195  df-hlat 33304
This theorem is referenced by:  hlol  33314  hlomcmat  33317  poml4N  33905  doca2N  35079  djajN  35090  dihoml4c  35329
  Copyright terms: Public domain W3C validator