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;
reserve o,m for set;

theorem Th9:
  for a,b being Object of 1Cat(o,m) for f being Morphism of 1Cat(o,m)
   holds f in Hom(a,b)
proof
  let a,b be Object of 1Cat(o,m);
  let f be Morphism of 1Cat(o,m);
  dom f = o by TARSKI:def 1;
  then dom f = a & cod f = b by TARSKI:def 1;
  hence thesis;
end;
