theorem Th24:
  p,q,r are_collinear implies p,r,q are_collinear & q,p,r
  are_collinear & r,q,p are_collinear & r,p,q are_collinear &
  q,r,p are_collinear
proof
  assume p,q,r are_collinear;
  then consider u,v,w such that
A1: p = Dir(u) & q = Dir(v) & r = Dir(w) & u is not zero & v is not zero
  & w is not zero and
A2: u,v,w are_LinDep by Th23;
A3: w,v,u are_LinDep & w,u,v are_LinDep by A2,ANPROJ_1:5;
A4: v,w,u are_LinDep by A2,ANPROJ_1:5;
  u,w,v are_LinDep & v,u,w are_LinDep by A2,ANPROJ_1:5;
  hence thesis by A1,A3,A4,Th23;
end;
