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Theorem hlomcmcv 32355
 Description: A Hilbert lattice is orthomodular, complete, and has the covering (exchange) property. (Contributed by NM, 5-Nov-2012.)
Assertion
Ref Expression
hlomcmcv

Proof of Theorem hlomcmcv
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eqid 2402 . . 3
2 eqid 2402 . . 3
3 eqid 2402 . . 3
4 eqid 2402 . . 3
5 eqid 2402 . . 3
6 eqid 2402 . . 3
7 eqid 2402 . . 3
81, 2, 3, 4, 5, 6, 7ishlat1 32351 . 2
98simplbi 458 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 367   w3a 974   wcel 1842   wne 2598  wral 2753  wrex 2754   class class class wbr 4394  cfv 5525  (class class class)co 6234  cbs 14733  cple 14808  cplt 15786  cjn 15789  cp0 15883  cp1 15884  ccla 15953  coml 32174  catm 32262  clc 32264  chlt 32349 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ral 2758  df-rex 2759  df-rab 2762  df-v 3060  df-dif 3416  df-un 3418  df-in 3420  df-ss 3427  df-nul 3738  df-if 3885  df-sn 3972  df-pr 3974  df-op 3978  df-uni 4191  df-br 4395  df-iota 5489  df-fv 5533  df-ov 6237  df-hlat 32350 This theorem is referenced by:  hloml  32356  hlclat  32357  hlcvl  32358  cvr1  32408  cvrp  32414  atcvr1  32415  atcvr2  32416
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