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

Theorem ollat 30073
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 30072 . 2  |-  ( K  e.  OL  <->  ( K  e.  Lat  /\  K  e.  OP ) )
21simplbi 448 1  |-  ( K  e.  OL  ->  K  e.  Lat )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1726   Latclat 14476   OPcops 30032   OLcol 30034
This theorem is referenced by:  oldmm1  30077  oldmj1  30081  olj01  30085  olj02  30086  olm12  30088  latmassOLD  30089  latm12  30090  latm32  30091  latmrot  30092  latm4  30093  latmmdiN  30094  latmmdir  30095  olm01  30096  olm02  30097  omllat  30102  meetat  30156
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-in 3329  df-ol 30038
  Copyright terms: Public domain W3C validator