
theorem Th15:
  for C,D being with_identities CategoryStr st C ~= D & C is empty
  holds D is empty
  proof
    let C,D be with_identities CategoryStr;
    assume C ~= D;
    then
A1: card Mor C = card Mor D by Th14;
    assume C is empty;
    hence D is empty by A1;
  end;
