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Theorem hloml 33310
 Description: A Hilbert lattice is orthomodular. (Contributed by NM, 20-Oct-2011.)
Assertion
Ref Expression
hloml

Proof of Theorem hloml
StepHypRef Expression
1 hlomcmcv 33309 . 2
21simp1d 1000 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wcel 1758  ccla 15381  coml 33128  clc 33218  chlt 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
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