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 Th4:
  for f being Morphism of a,b st Hom(a,b) <> {} holds dom(f) = a & cod(f) = b
proof
  let f be Morphism of a,b;
  assume Hom(a,b) <> {};
  then f in Hom(a,b) by Def3;
  hence thesis by Th1;
end;
