Twenty-second Amendment to the United States Constitution
Some argue that the 22nd Amendment and 12th Amendment bar any two-term president from later serving as vice president as well as from succeeding to the presidency from any point in the presidential line of succession. Others contend that the original intent of the 12th Amendment concerns qualification for "service" (age, residence, and citizenship), while the 22nd Amendment, concerns qualifications for "election", and thus (strictly applying the text) a former two-term president is still eligible to "serve" as vice president (neither amendment restricts the number of times an individual can be elected to the vice presidency), and then succeed to the presidency to serve out the balance of the term (though prohibited from running for election to an additional term).
William Henry Harrison
Harrison's cabinet insisted that Tyler was "Vice President acting as President". After the cabinet consulted with the Chief Justice Roger Taney, they decided that if Tyler took the presidential Oath of Office, he would assume the office of president. Tyler obliged and was sworn into office on April 6, 1841. Congress convened in May, and after a short period of debate in both houses, it passed a resolution that confirmed Tyler as president for the remainder of Harrison's term. Once established, this precedent of presidential succession remained in effect until the Twenty-fifth Amendment was ratified in 1967, following the assassination of John F. Kennedy and the succession of Lyndon B. Johnson to the presidency in 1963. The Twenty-fifth Amendment dealt with the finer points of succession, defining the situations in which the vice president would serve as acting president, and in which situations the vice president could become president.