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 = R | (dom R /\ X)
proof
  thus R | X = (R | dom R) | X
    .= R | (dom R /\ X) by Th65;
end;
