
theorem Th7:
  for M being MetrSpace, x,y being Element of M st x <> y holds 0 < dist(x,y)
proof
  let M be MetrSpace;
  let x,y be Element of M;
A1:  dist(x,y) >= 0 by Th5;
  assume x <> y;
  then dist(x,y) <> 0 by Th2;
  hence thesis by A1,XXREAL_0:1;
end;
