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
  R|X = (id X)*R
proof
  let x,y;
  [x,y] in R|X iff [x,y] in R & x in X by Def9;
  hence thesis by Th42;
end;
