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

Theorem ollat 29379
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 29378 . 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 1717   Latclat 14394   OPcops 29338   OLcol 29340
This theorem is referenced by:  oldmm1  29383  oldmj1  29387  olj01  29391  olj02  29392  olm12  29394  latmassOLD  29395  latm12  29396  latm32  29397  latmrot  29398  latm4  29399  latmmdiN  29400  latmmdir  29401  olm01  29402  olm02  29403  omllat  29408  meetat  29462
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 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-v 2894  df-in 3263  df-ol 29344
  Copyright terms: Public domain W3C validator