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Theorem cvllat 30138
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 30137 . 2  |-  ( K  e.  CvLat  ->  K  e.  AtLat
)
2 atllat 30112 . 2  |-  ( K  e.  AtLat  ->  K  e.  Lat )
31, 2syl 15 1  |-  ( K  e.  CvLat  ->  K  e.  Lat )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1696   Latclat 14167   AtLatcal 30076   CvLatclc 30077
This theorem is referenced by:  cvlposN  30139  cvlexch2  30141  cvlexchb1  30142  cvlexchb2  30143  cvlatexchb2  30147  cvlatexch1  30148  cvlatexch2  30149  cvlatexch3  30150  cvlcvr1  30151  cvlcvrp  30152  cvlatcvr2  30154  cvlsupr2  30155  cvlsupr7  30160  cvlsupr8  30161
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-iota 5235  df-fv 5279  df-ov 5877  df-atl 30110  df-cvlat 30134
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