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Question:

Why is it not permitted by you to say "Ali-un-Waliullah" in azan?
If we don’t say this, what is the difference between us and the others?

Answer:

It is established through all Shia books of Hadith, Fiqh, etc. that the azaan which was made a creed by Allah, which Allah then revealed through Jibrail (AS) to the Holy Prophet (SAWAW), which the Prophet (SAWAW) first taught to Hazrat Ali (AS), which Hazrat Ali (AS) then taught to Hazrat Bilal (RA) and he continued to pronounce it until the demise of the Holy Prophet (SAWAW), that azaan consisted of 18 sentences i.e. this sentence was not included in it.
It was the azaan which the Imams of Ahl-e-Bait (AS), starting from Hazrat Imam Ali (AS) until the Ghaibat-e-Kubra of Hazrat Imam Mahdi (AS), used to pronounce and let others pronounce. Therefore, we also pronounce the same azaan.
As far as difference with others is concerned, the difference of "Hayya ala khair-il-amal" is enough. For us it is an integral part of azaan, while the Sunni brothers have excluded it from azaan.