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Theorem cvllat 30186
Description: An atomic lattice with the covering property is a lattice. (Contributed by NM, 5-Nov-2012.)
Assertion
Ref Expression
cvllat  |-  ( K  e.  CvLat  ->  K  e.  Lat )

Proof of Theorem cvllat
StepHypRef Expression
1 cvlatl 30185 . 2  |-  ( K  e.  CvLat  ->  K  e.  AtLat
)
2 atllat 30160 . 2  |-  ( K  e.  AtLat  ->  K  e.  Lat )
31, 2syl 16 1  |-  ( K  e.  CvLat  ->  K  e.  Lat )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1726   Latclat 14476   AtLatcal 30124   CvLatclc 30125
This theorem is referenced by:  cvlposN  30187  cvlexch2  30189  cvlexchb1  30190  cvlexchb2  30191  cvlatexchb2  30195  cvlatexch1  30196  cvlatexch2  30197  cvlatexch3  30198  cvlcvr1  30199  cvlcvrp  30200  cvlatcvr2  30202  cvlsupr2  30203  cvlsupr7  30208  cvlsupr8  30209
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-ne 2603  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-atl 30158  df-cvlat 30182
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