
theorem
  for f being continuous one-to-one Function of I[01], I[01] st f.0 = 0
& f.1 = 1 holds for x, y being Point of I[01],
   p, q, fx, fy being Real st x = p
  & y = q & p < q & fx = f.x & fy = f.y holds fx < fy by Th15,TOPMETR:20;
