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Theorem cvllat 29516
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 29515 . 2  |-  ( K  e.  CvLat  ->  K  e.  AtLat
)
2 atllat 29490 . 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 1684   Latclat 14151   AtLatcal 29454   CvLatclc 29455
This theorem is referenced by:  cvlposN  29517  cvlexch2  29519  cvlexchb1  29520  cvlexchb2  29521  cvlatexchb2  29525  cvlatexch1  29526  cvlatexch2  29527  cvlatexch3  29528  cvlcvr1  29529  cvlcvrp  29530  cvlatcvr2  29532  cvlsupr2  29533  cvlsupr7  29538  cvlsupr8  29539
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-ne 2448  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-atl 29488  df-cvlat 29512
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