
theorem Th21:
  for C being non empty with_identities composable CategoryStr,
      a being Object of C holds a in Hom(a,a)
  proof
    let C be non empty with_identities composable CategoryStr;
    let a be Object of C;
    a in Ob C;
    then reconsider f = a as morphism of C;
    f is identity by CAT_6:22;
    then dom f = f & cod f = f by Th6;
    hence a in Hom(a,a);
  end;
