Users' Mathboxes Mathbox for Norm Megill < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  ollat Unicode version

Theorem ollat 29708
Description: An ortholattice is a lattice. (Contributed by NM, 18-Sep-2011.)
Assertion
Ref Expression
ollat  |-  ( K  e.  OL  ->  K  e.  Lat )

Proof of Theorem ollat
StepHypRef Expression
1 isolat 29707 . 2  |-  ( K  e.  OL  <->  ( K  e.  Lat  /\  K  e.  OP ) )
21simplbi 447 1  |-  ( K  e.  OL  ->  K  e.  Lat )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1721   Latclat 14437   OPcops 29667   OLcol 29669
This theorem is referenced by:  oldmm1  29712  oldmj1  29716  olj01  29720  olj02  29721  olm12  29723  latmassOLD  29724  latm12  29725  latm32  29726  latmrot  29727  latm4  29728  latmmdiN  29729  latmmdir  29730  olm01  29731  olm02  29732  omllat  29737  meetat  29791
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 2393
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-v 2926  df-in 3295  df-ol 29673
  Copyright terms: Public domain W3C validator