The Kharijites believed that faith was demonstrated in righteous acts and that without making faith explicit in public behavior; one could not claim to be a Muslim. They also thought that sinful acts committed by any Muslim, including the khalīfah, breached one's confession of faith and one's claim to be a Muslim. They based their conclusion on certain pronouncements in the Quran in which infidelity is related to some major acts of moral transgression through the use of such phrases as "there is no faith in him, ""he does not belong to us," and "he has no place in Islam" to censure the conduct of the person who is guilty of such acts or to indicate the punishment of hell which is promised to him. The Khārijites argued that the caliph 'Uthmān had acted contrary to the mandate of the Sharī'ah: therefore, he and all those who committed grave sins should be expelled from the Islamic ummah. Initially they supported 'Alī in his struggle for the caliphate against Mu'āwiyah, but when 'Ali lost in the arbitration between him and Mu'awiyah on the matter of the caliphate, the Khārijites withdrew from his forces to form a separate sect.