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Theorem hlcvl 30157
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 30154 . 2  |-  ( K  e.  HL  ->  ( K  e.  OML  /\  K  e.  CLat  /\  K  e.  CvLat
) )
21simp3d 971 1  |-  ( K  e.  HL  ->  K  e.  CvLat )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1725   CLatccla 14536   OMLcoml 29973   CvLatclc 30063   HLchlt 30148
This theorem is referenced by:  hlatl  30158  hlexch1  30179  hlexch2  30180  hlexchb1  30181  hlexchb2  30182  hlsupr2  30184  hlexch3  30188  hlexch4N  30189  hlatexchb1  30190  hlatexchb2  30191  hlatexch1  30192  hlatexch2  30193  llnexchb2lem  30665  4atexlemkc  30855  4atex  30873  4atex3  30878  cdleme02N  31019  cdleme0ex2N  31021  cdleme0moN  31022  cdleme0nex  31087  cdleme20zN  31098  cdleme20y  31099  cdleme19a  31100  cdleme19d  31103  cdleme21a  31122  cdleme21b  31123  cdleme21c  31124  cdleme21ct  31126  cdleme22f  31143  cdleme22f2  31144  cdleme22g  31145  cdlemf1  31358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-iota 5418  df-fv 5462  df-ov 6084  df-hlat 30149
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