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
  P c= R & X c= Y implies P.:X c= R.:Y
proof
  assume P c= R & X c= Y;
  then P.:X c= R.:X & R.:X c= R.:Y by Th115,Th116;
  hence thesis;
end;
