reserve X,Y,x for set;
reserve A for non empty preBoolean set;

theorem Th14:
  for A being set st A is finite holds Fin A = bool A
proof
  let A be set;
  assume
A1: A is finite;
A2: bool A c= Fin A
  by A1,Def5;
  Fin A c= bool A by Th13;
  hence thesis by A2;
end;
