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 Th22:
  for f being Function holds rng("f) c= bool dom f
proof
  let f be Function;
  let x be object;
   reconsider xx=x as set by TARSKI:1;
  assume x in rng("f);
  then consider y being object such that
A1: y in dom("f) & x = "f.y by FUNCT_1:def 3;
   reconsider y as set by TARSKI:1;
  x = f"y by A1,Th21;
  then xx c= dom f by RELAT_1:132;
  hence thesis;
end;
