theorem
  for x,y,z being Element of X st x in singleton X.z & y in singleton X.
  z holds x = y
proof
  let x,y,z be Element of X;
  assume that
A1: x in singleton X.z and
A2: y in singleton X.z;
  x = z by A1,Th52;
  hence thesis by A2,Th52;
end;
