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Theorem isatliN 30100
 Description: Properties that determine an atomic lattice. (Contributed by NM, 18-Sep-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
isatlati.1
isatlati.b
isatlati.l
isatlati.z
isatlati.a
isatlati.6
isatlati.7
Assertion
Ref Expression
isatliN
Distinct variable groups:   ,   ,   ,,
Allowed substitution hints:   ()   ()   (,)   (,)

Proof of Theorem isatliN
StepHypRef Expression
1 isatlati.1 . 2
2 isatlati.6 . 2
3 isatlati.7 . . . 4
43ex 424 . . 3
54rgen 2771 . 2
6 isatlati.b . . 3
7 isatlati.l . . 3
8 isatlati.z . . 3
9 isatlati.a . . 3
106, 7, 8, 9isatl 30097 . 2
111, 2, 5, 10mpbir3an 1136 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725   wne 2599  wral 2705  wrex 2706   class class class wbr 4212  cfv 5454  cbs 13469  cple 13536  cp0 14466  clat 14474  catm 30061  cal 30062 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-iota 5418  df-fv 5462  df-atl 30096
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