Did Ali ever say that only house of Muhamad can rule muslims?

Wikipedia seems to say so > After Ali's death, Kufi Muslims pledged allegiance to his eldest son > Hasan without dispute, as Ali on many occasions had declared that just > People of the House of Muhammad were entitled to rule the Muslim > community. At this time, Muawiyah held both the Levant and Egypt > and, as commander of the largest force in the Muslim Empire, had > declared himself caliph and marched his army into Iraq, the seat of > Hasan's caliphate. https://en.wikipedia.org/wiki/Ali That seems like the cornerstone of the Shia beliefs right? Is this something the Sunnis believe in too? This question is reasked here https://history.stackexchange.com/questions/58430/did-ali-say-that-only-muhammads-descendants-can-rule