reserve a,b,c,d for Ordinal;
reserve l for non empty limit_ordinal Ordinal;
reserve u for Element of l;
reserve A for non empty Ordinal;
reserve e for Element of A;
reserve X,Y,x,y,z for set;
reserve n,m for Nat;

theorem Th2:
  X is ordinal-membered iff On X = X
  proof
    hereby assume
A1:   X is ordinal-membered;
      thus On X = X
      proof thus On X c= X by ORDINAL2:7;
        let x be object;
        thus thesis by A1,ORDINAL1:def 9;
      end;
    end;
    thus thesis;
  end;
