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
  X c= dom R implies dom(R|X) = X
proof
  dom(R|X) = dom R /\ X by Th55;
  hence thesis by XBOOLE_1:28;
end;
