reserve X for set;
reserve UN for Universe;

theorem
  for X being set,Y being non empty set, f being Function of X,Y st
  f in UN holds X in UN
  proof
    let X be set;
    let Y be non empty set;
    let f be Function of X,Y;
    assume
A1: f in UN;
    dom f = X by FUNCT_2:def 1;
    hence thesis by A1,Th37;
  end;
