theorem
  for CS being non empty CollStr holds CS is 2-dimensional
  CollProjectiveSpace iff (CS is at_least_3rank proper CollSp & for p,p1,q,q1
  being Element of CS ex r being Element of CS st p,p1,r are_collinear & q,q1,r
  are_collinear)
proof
  let CS be non empty CollStr;
  thus CS is 2-dimensional CollProjectiveSpace implies CS is at_least_3rank
proper CollSp & for p,p1,q,q1 being Element of CS ex r being Element of CS st p
  ,p1,r are_collinear & q,q1,r are_collinear by Def14;
  assume that
A1: CS is at_least_3rank proper CollSp and
A2: for p,p1,q,q1 being Element of CS ex r being Element of CS st p,p1,r
  are_collinear & q,q1,r are_collinear;
  CS is Vebleian
  by A2;
  hence thesis by A1,A2,Def14;
end;
