If a man passes wind then he goes to wash up (Wudu) for praying with out washing ones anus is that okay or not?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions. An-Nawawi , may Allah be pleased with him, in his book entitled 'Al-Majmou', proclaimed that it is not an obligation that one makes Istinjaa' (cleaning his/her private parts) upon passing wind. He said: Jurists unanimously held the opinion that it is not incumbent upon the person to makes Istinjaa' because of passing wind, sleeping, touching women, or touching one's sexual organ . And not only that; rather they (jurists) said that making Istinjaa' upon passing wind is hateful. Hereby, it has become clear that making Istinjaa' upon passing wind is not a matter of obligation for it (wind broken) is not impure. Jurists often, upon speaking about this ruling (the non-obligation of making Istinjaa' upon breaking wind) cite the following Hadith (Prophet's saying): He who makes Istinjaa' after passing wind is not among (belonging to) us (Muslims) . But this Hadith is weak. Allah knows best.