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Theorem cvllat 34926
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 34925 . 2  |-  ( K  e.  CvLat  ->  K  e.  AtLat
)
2 atllat 34900 . 2  |-  ( K  e.  AtLat  ->  K  e.  Lat )
31, 2syl 16 1  |-  ( K  e.  CvLat  ->  K  e.  Lat )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1804   Latclat 15654   AtLatcal 34864   CvLatclc 34865
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 976  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-ne 2640  df-ral 2798  df-rex 2799  df-rab 2802  df-v 3097  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3771  df-if 3927  df-sn 4015  df-pr 4017  df-op 4021  df-uni 4235  df-br 4438  df-dm 4999  df-iota 5541  df-fv 5586  df-ov 6284  df-atl 34898  df-cvlat 34922
This theorem is referenced by:  cvlposN  34927  cvlexch2  34929  cvlexchb1  34930  cvlexchb2  34931  cvlatexchb2  34935  cvlatexch1  34936  cvlatexch2  34937  cvlatexch3  34938  cvlcvr1  34939  cvlcvrp  34940  cvlatcvr2  34942  cvlsupr2  34943  cvlsupr7  34948  cvlsupr8  34949
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