  In this note we generalize the Moroianu's fixed point theorem. We propose a
very elegant common proof of the Bourbaki's fixed point theorem and our result.
We apply our result to give a very elegant proof of the fact that, in the
Zermelo-Fraenkel system, the axiom of choice is equivalent to each of the
following statements: H. Kneser's Lemma, Zorn's Lemma, Zermelo's Lemma
