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Theorem cvlatl 30124
 Description: An atomic lattice with the covering property is an atomic lattice. (Contributed by NM, 5-Nov-2012.)
Assertion
Ref Expression
cvlatl

Proof of Theorem cvlatl
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eqid 2437 . . 3
2 eqid 2437 . . 3
3 eqid 2437 . . 3
4 eqid 2437 . . 3
51, 2, 3, 4iscvlat 30122 . 2
65simplbi 448 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 360   wcel 1726  wral 2706   class class class wbr 4213  cfv 5455  (class class class)co 6082  cbs 13470  cple 13537  cjn 14402  catm 30062  cal 30063  clc 30064 This theorem is referenced by:  cvllat  30125  cvlexch3  30131  cvlexch4N  30132  cvlatexchb1  30133  cvlcvr1  30138  cvlcvrp  30139  cvlatcvr1  30140  cvlsupr2  30142  hlatl  30159 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ral 2711  df-rex 2712  df-rab 2715  df-v 2959  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-op 3824  df-uni 4017  df-br 4214  df-iota 5419  df-fv 5463  df-ov 6085  df-cvlat 30121
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