reserve AS for AffinSpace;
reserve a,a9,b,b9,c,d,o,p,q,r,s,x,y,z,t,u,w for Element of AS;

theorem
  x<>y implies ex z st not LIN x,y,z
proof
  assume
A1: x<>y;
  consider a,b,c such that
A2: not LIN a,b,c by Th11;
  assume
A3: not thesis;
  then
A4: LIN x,y,b;
A5: LIN x,y,c by A3;
  LIN x,y,a by A3;
  hence contradiction by A1,A2,A4,A5,Th7;
end;
