reserve p,q,x,x1,x2,y,y1,y2,z,z1,z2 for set;
reserve A,B,V,X,X1,X2,Y,Y1,Y2,Z for set;
reserve C,C1,C2,D,D1,D2 for non empty set;

theorem Th19:
  for f being Function holds .:f is Function of bool dom f, bool rng f
proof
  let f be Function;
  dom .:f = bool dom f & rng.:f c= bool rng f by Def1,Th9;
  hence thesis by FUNCT_2:def 1,RELSET_1:4;
end;
