theorem
  for X being strict non empty MetrSpace holds the distance of X is
  Reflexive discerning symmetric triangle
proof
  let X be strict non empty MetrSpace;
A1: the distance of X is_metric_of the carrier of X by PCOMPS_1:35;
  hence the distance of X is Reflexive by Th3;
  thus the distance of X is discerning by A1,Th3;
  thus the distance of X is symmetric by A1,Th3;
  thus thesis by A1,Th3;
end;
