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Theorem omlol 30040
 Description: An orthomodular lattice is an ortholattice. (Contributed by NM, 18-Sep-2011.)
Assertion
Ref Expression
omlol

Proof of Theorem omlol
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eqid 2438 . . 3
2 eqid 2438 . . 3
3 eqid 2438 . . 3
4 eqid 2438 . . 3
5 eqid 2438 . . 3
61, 2, 3, 4, 5isoml 30038 . 2
76simplbi 448 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1653   wcel 1726  wral 2707   class class class wbr 4214  cfv 5456  (class class class)co 6083  cbs 13471  cple 13538  coc 13539  cjn 14403  cmee 14404  col 29974  coml 29975 This theorem is referenced by:  omlop  30041  omllat  30042  omllaw3  30045  omllaw4  30046  cmtcomlemN  30048  cmtbr2N  30053  cmtbr3N  30054  omlfh1N  30058  omlfh3N  30059  omlspjN  30061  hlol  30161 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-iota 5420  df-fv 5464  df-ov 6086  df-oml 29979
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