
theorem Th2:
  for C being with_identities CategoryStr, a being Object of C
  st C is non empty holds a in the carrier of C
  proof
    let C be with_identities CategoryStr;
    let a be Object of C;
    assume C is non empty;
    then a in Ob C by SUBSET_1:def 1;
    then a in Mor C;
    hence a in the carrier of C by CAT_6:def 1;
  end;
