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Theorem cvllat 33998
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 33997 . 2  |-  ( K  e.  CvLat  ->  K  e.  AtLat
)
2 atllat 33972 . 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 1762   Latclat 15521   AtLatcal 33936   CvLatclc 33937
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 970  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2446  df-cleq 2452  df-clel 2455  df-nfc 2610  df-ne 2657  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3108  df-dif 3472  df-un 3474  df-in 3476  df-ss 3483  df-nul 3779  df-if 3933  df-sn 4021  df-pr 4023  df-op 4027  df-uni 4239  df-br 4441  df-dm 5002  df-iota 5542  df-fv 5587  df-ov 6278  df-atl 33970  df-cvlat 33994
This theorem is referenced by:  cvlposN  33999  cvlexch2  34001  cvlexchb1  34002  cvlexchb2  34003  cvlatexchb2  34007  cvlatexch1  34008  cvlatexch2  34009  cvlatexch3  34010  cvlcvr1  34011  cvlcvrp  34012  cvlatcvr2  34014  cvlsupr2  34015  cvlsupr7  34020  cvlsupr8  34021
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