Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  dlatl Structured version   Unicode version

Theorem dlatl 14621
 Description: A distributive lattice is a lattice. (Contributed by Stefan O'Rear, 30-Jan-2015.)
Assertion
Ref Expression
dlatl DLat

Proof of Theorem dlatl
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eqid 2436 . . 3
2 eqid 2436 . . 3
3 eqid 2436 . . 3
41, 2, 3isdlat 14619 . 2 DLat
54simplbi 447 1 DLat
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  wral 2705  cfv 5454  (class class class)co 6081  cbs 13469  cjn 14401  cmee 14402  clat 14474  DLatcdlat 14617 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  ax-nul 4338 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-eu 2285  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-sbc 3162  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-ov 6084  df-dlat 14618
 Copyright terms: Public domain W3C validator