reserve x,x1,x2,y,y9,y1,y2,z,z1,z2 for object,P,X,X1,X2,Y,Y1,Y2,V,Z for set;

theorem Th14:
  for f being Function holds Y|`f|X is PartFunc of X,Y
proof
  let f be Function;
  Y|`f|X = Y|`(f|X) by RELAT_1:109;
  then dom(Y|`f|X) c= X & rng(Y|`f|X) c= Y by RELAT_1:58,85;
  hence thesis by RELSET_1:4;
end;
