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Theorem cvllat 33279
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 33278 . 2  |-  ( K  e.  CvLat  ->  K  e.  AtLat
)
2 atllat 33253 . 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 1758   Latclat 15319   AtLatcal 33217   CvLatclc 33218
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-ne 2646  df-ral 2800  df-rex 2801  df-rab 2804  df-v 3072  df-dif 3431  df-un 3433  df-in 3435  df-ss 3442  df-nul 3738  df-if 3892  df-sn 3978  df-pr 3980  df-op 3984  df-uni 4192  df-br 4393  df-dm 4950  df-iota 5481  df-fv 5526  df-ov 6195  df-atl 33251  df-cvlat 33275
This theorem is referenced by:  cvlposN  33280  cvlexch2  33282  cvlexchb1  33283  cvlexchb2  33284  cvlatexchb2  33288  cvlatexch1  33289  cvlatexch2  33290  cvlatexch3  33291  cvlcvr1  33292  cvlcvrp  33293  cvlatcvr2  33295  cvlsupr2  33296  cvlsupr7  33301  cvlsupr8  33302
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