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

Theorem hlcvl 29549
Description: A Hilbert lattice is an atomic lattice with the covering property. (Contributed by NM, 5-Nov-2012.)
Assertion
Ref Expression
hlcvl  |-  ( K  e.  HL  ->  K  e.  CvLat )

Proof of Theorem hlcvl
StepHypRef Expression
1 hlomcmcv 29546 . 2  |-  ( K  e.  HL  ->  ( K  e.  OML  /\  K  e.  CLat  /\  K  e.  CvLat
) )
21simp3d 969 1  |-  ( K  e.  HL  ->  K  e.  CvLat )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1684   CLatccla 14213   OMLcoml 29365   CvLatclc 29455   HLchlt 29540
This theorem is referenced by:  hlatl  29550  hlexch1  29571  hlexch2  29572  hlexchb1  29573  hlexchb2  29574  hlsupr2  29576  hlexch3  29580  hlexch4N  29581  hlatexchb1  29582  hlatexchb2  29583  hlatexch1  29584  hlatexch2  29585  llnexchb2lem  30057  4atexlemkc  30247  4atex  30265  4atex3  30270  cdleme02N  30411  cdleme0ex2N  30413  cdleme0moN  30414  cdleme0nex  30479  cdleme20zN  30490  cdleme20y  30491  cdleme19a  30492  cdleme19d  30495  cdleme21a  30514  cdleme21b  30515  cdleme21c  30516  cdleme21ct  30518  cdleme22f  30535  cdleme22f2  30536  cdleme22g  30537  cdlemf1  30750
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-iota 5219  df-fv 5263  df-ov 5861  df-hlat 29541
  Copyright terms: Public domain W3C validator