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 Th71:
  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 Th69,Th70;
  hence thesis;
end;
