reserve FCPS for up-3-dimensional CollProjectiveSpace;
reserve a,a9,b,b9,c,c9,d,d9,o,p,q,r,s,t,u,x,y,z for Element of FCPS;

theorem
  ex q,r st not p,q,r are_collinear
proof
  consider q such that
A1: p<>q and
  p<>q and
  p,p,q are_collinear by ANPROJ_2:def 10;
  ex r st not p,q,r are_collinear by A1,COLLSP:12;
  hence thesis;
end;
