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Theorem atl0cl 29786
 Description: An atomic lattice has a zero element. We can use this in place of op0cl 29667 for lattices without orthocomplements. (Contributed by NM, 5-Nov-2012.)
Hypotheses
Ref Expression
atl0cl.b
atl0cl.z
Assertion
Ref Expression
atl0cl

Proof of Theorem atl0cl
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 atl0cl.b . . 3
2 eqid 2404 . . 3
3 atl0cl.z . . 3
4 eqid 2404 . . 3
51, 2, 3, 4isatl 29782 . 2
65simp2bi 973 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1649   wcel 1721   wne 2567  wral 2666  wrex 2667   class class class wbr 4172  cfv 5413  cbs 13424  cple 13491  cp0 14421  clat 14429  catm 29746  cal 29747 This theorem is referenced by:  atl0le  29787  atlle0  29788  atlltn0  29789  isat3  29790  atnle0  29792  atlen0  29793  atcmp  29794  atcvreq0  29797  pmap0  30247  dia0  31535  dih0cnv  31766 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ne 2569  df-ral 2671  df-rex 2672  df-rab 2675  df-v 2918  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-nul 3589  df-if 3700  df-sn 3780  df-pr 3781  df-op 3783  df-uni 3976  df-br 4173  df-iota 5377  df-fv 5421  df-atl 29781
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