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) holds Hom(a,b) <> {} by Th9;
