theorem Th4:
  F is commutative implies F/\/RD is commutative
proof
  defpred P[Element of Class RD, Element of Class RD] means (F/\/RD).($1,$2) =
  (F/\/RD).($2,$1);
  assume
A1: for a,b holds F.(a,b) = F.(b,a);
A2: now
    let x1,x2 be Element of D;
    (F/\/RD).(EqClass(RD,x1),EqClass(RD,x2)) = Class(RD, F.(x1,x2)) by Th3
      .= Class(RD, F.(x2,x1)) by A1
      .= (F/\/RD).(EqClass(RD,x2),EqClass(RD,x1)) by Th3;
    hence P[EqClass(RD,x1),EqClass(RD,x2)];
  end;
  thus for c1,c2 being Element of Class RD holds P[c1,c2] from SchAux2( A2);
end;
