reserve C for CatStr;
reserve f,g for Morphism of C;
reserve C for non void non empty CatStr,
  f,g for Morphism of C,
  a,b,c,d for Object of C;

theorem Th6:
  for f being Morphism of a,b st Hom(a,b) = {f} for g being
  Morphism of a,b holds f = g
proof
  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,Def3;
  hence thesis by TARSKI:def 1;
end;
