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 Th4:
  for f being Y-valued Function st x in dom f holds f.x in Y
proof
  let f be Y-valued Function;
  assume x in dom f;
  then
A1: f.x in rng f by FUNCT_1:def 3;
  rng f c= Y by RELAT_1:def 19;
  hence thesis by A1;
end;
