reserve X for set;
reserve UN for Universe;

theorem Th20:
  not UN is denumerable iff omega in UN
  proof
    hereby
      assume not UN is denumerable;
      then UN is uncountable;
      hence omega in UN by ORDINAL6:57;
    end;
    assume omega in UN;
    hence not UN is denumerable by ORDINAL6:57;
  end;
