
theorem Th6:
  for C being CategoryStr, a,b being Object of C
  for f being Morphism of a,b st Hom(a,b) = {f} for g being
  Morphism of a,b holds f = g
proof
  let C be CategoryStr, a,b be Object of C;
  let f be Morphism of a,b such that
A1: Hom(a,b) = {f};
  let g be Morphism of a,b;
  g in {f} by A1,CAT_7:def 3;
  hence thesis by TARSKI:def 1;
end;
