Our branch of Shia Islam, in that particular generation of the family, accepted the legitimacy of the eldest son, Isma‘il, as being the appointed Imam to succeed and that is why they are known as Ismailis.
(Forty-Ninth Hereditary Imam of the Shi‘i Isma‘ili Muslims)
Taken individually or collectively, these Seven Proofs demonstrate that the legitimate successor and true Imam after the Imam Ja‘far al-Sadiq is Mawlana Isma‘il ibn Ja‘far and that the Present and Living Imam of all Shi‘i Muslims must be the direct lineal descendant of Isma‘il ibn Ja‘far.
Proof #1: Imām Ja‘far designated Mawlānā Ismā‘īl as the next Imam by the rule of nass as per Twelver, Ismaili, Sunni and academic sources.
Proof #2: The only way to deny the nass of Mawlānā Isma‘il is through contradictoryhadiths presented in later Twelver hadith books.
Proof #3: Isma‘il’s death before Imam Ja‘far is not confirmed and may have been staged to protect him — as he was reportedly seen by eyewitnesses after his alleged death.
Proof #4: Even if Isma‘il had died before his father, the Imamat continued in Isma‘il’s son, Muhammad ibn Isma‘il, whom Isma‘il had appointed as his own successor.
Proof #5: Earliest Shi‘i hadiths lack the mention of Twelve Imams but instead predict exactly the first eighteen Imams in the Isma‘ili lineage of Imamat.
Proof #6: With the exception of the Nizari Ismaili Imamat, all other Shi‘i Imamat lineages have hidden Imams. This contradicts the Qur’anic definition of Imamat which requires the Imam always be present and manifest (mubin) in the world.
Proof #7: Imam Shah Karim al-Husayni Aga Khan IV is the forty-ninth hereditary Imam of Shi‘i Islam in direct, documented, lineal descent from Mawlana Isma‘il ibn Ja‘far al-Sadiq. As the only present (hadir), manifest (mubin) and living (mawjud) hereditary Imam, with a documented and validated lineage, Imam Shah Karim al-Husayni’s very existence is itself confirmation of his Imamat and that of his ancestors.
Click here to read at the source: http://ismailignosis.com/2014/10/02/who-succeeded-imam-jafar-al-sadiq-seven-proofs-for-the-imamat-of-imam-ismail-ibn-jafar/
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