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During the rule of the succeeding Hanoverian dynasty, power was gradually exercised more by parliament and the government. The first Hanoverian monarch, George I, relied on his ministers to a greater extent than did previous monarchs. Later Hanoverian monarchs attempted to restore royal control over legislation: George III and George IV both openly opposed Catholic Emancipation and asserted that to grant assent to a Catholic emancipation bill would violate the Coronation Oath, which required the sovereign to preserve and protect the established Church of England from Papal domination and would grant rights to individuals who were in league with a foreign power which did not recognise their legitimacy. However, George IV reluctantly granted his assent upon the advice of his ministers. Thus, as the concept of ministerial responsibility has evolved, the power to withhold royal assent has fallen into disuse, both in the United Kingdom and in the other Commonwealth realms.

What rule did George III and George IV believe a Catholic emancipation bill would violate?
Coronation Oath