reserve SAS for Semi_Affine_Space;
reserve a,a9,a1,a2,a3,a4,b,b9,c,c9,d,d9,d1,d2,o,p,p1,p2,q,r,r1,r2,s,x, y,t,z
  for Element of SAS;

theorem
  not o,a,b are_collinear & o,a,x are_collinear & o,b,x are_collinear
    implies o=x
proof
  assume that
A1: not o,a,b are_collinear and
A2: o,a,x are_collinear and
A3: o,b,x are_collinear;
  b,o,x are_collinear by A3,Th22;
  then
A4: b,o // b,x;
  o,a // o,x by A2;
  then
A5: a,o // a,x by Th14;
  not a,b,o are_collinear by A1,Th22;
  then not a,b // a,o;
  hence thesis by A5,A4,Th18;
end;
