theorem Th26:
  Class(EqRel(S),x) = Class(EqRel(S),y) iff x,y Fr_Eq S
   proof
     set E = EqRel(S);
     thus Class(E,x) = Class(E,y) implies x,y Fr_Eq S
     proof
       assume Class(E,x) = Class(E,y);
       then x in Class(E,y) by EQREL_1:23;
       hence thesis by Th25;
     end;
     assume x,y Fr_Eq S;
     then x in Class(E,y) by Th25;
     hence thesis by EQREL_1:23;
  end;
