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
  for a,b being Object of 1Cat(o,m) for f being Morphism of 1Cat(o,m)
  holds f is Morphism of a,b
proof
  let a,b be Object of 1Cat(o,m);
  let f be Morphism of 1Cat(o,m);
  f in Hom(a,b) by Th9;
  hence thesis by Def3;
end;
