Mills proof of Utilitarianism

Mill's proof of Utilitarisnism - 

Mill aims to prove Utilitarianism by essential saying it is necessary for society. Though not necessary in the way God is according to Descartes. 

Mill says that if happiness if good to you, which it is, then it good for the 'aggregate of people'. In effect he claims because we seek our own happiness then i am also committed to the happiness of everyone else. This is contestable by saying…