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
  for f being Morphism of a,b st Hom(a,b),Hom(c,d) are_equipotent & Hom(
  a,b) = {f} holds ex h being Morphism of c,d st Hom(c,d) = {h}
proof
  let f be Morphism of a,b;
  assume Hom(a,b),Hom(c,d) are_equipotent;
  then consider F being Function such that
  F is one-to-one and
A1: dom F = Hom(a,b) & rng F = Hom(c,d) by WELLORD2:def 4;
  assume Hom(a,b) = {f};
  then
A2: Hom(c,d) = {F.f} by A1,FUNCT_1:4;
  then F.f in Hom(c,d) by TARSKI:def 1;
  then F.f is Morphism of c,d by Def3;
  hence thesis by A2;
end;
