reserve A,X,X1,X2,Y,Y1,Y2 for set, a,b,c,d,x,y,z for object;
reserve P,P1,P2,Q,R,S for Relation;

theorem
  Q|A = R|A implies Q.:A = R.:A
proof
  assume Q|A = R|A;
  hence Q.:A = (R|A).:A by Th121
  .= R.:A by Th121;
end;
