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
  Y c= rng R implies rng(Y|`R) = Y
proof
  assume Y c= rng R;
  then rng R /\ Y = Y by XBOOLE_1:28;
  hence thesis by Th82;
end;
