reserve x,y for set;
reserve X for non empty set;
reserve a,b,c,d for Element of X;
reserve S for OAffinSpace;
reserve a,b,c,d,p,q,r,x,y,z,t,u,w for Element of S;

theorem
  x<>y implies ex z st not x,y,z are_collinear
proof
  assume
A1: x<>y;
  consider a,b,c such that
A2: not a,b,c are_collinear by Th36;
  assume
A3: not thesis;
  then
A4: x,y,c are_collinear;
  x,y,a are_collinear & x,y,b are_collinear by A3;
  hence contradiction by A1,A2,A4,Th32;
end;
