As stated and ruled out by the major grand scholars such as Syed Khamanei that anything added in Salah even if it is a true statement is considered as an innovation and makes the prayer invalid. Regarding the third testimony in salah, why is that the third testimony is not recited by us Shia Muslims at the end of Salah in Tashahud when giving salams to the Prophet (PBUH) and what evidence indicates that it has been forbidden or that it was not done by the final Prophet (PBUH) or any of the 12 imams?

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The general law is that we cannot add anything in Salat except if it’s a Dua or prayer. We can make any prayer in Salat. The third testimony is not a Du’a, hence one cannot say unless there is an authentic hadith that says we can. There is a hadith, but many scholars have not considered it as an authentic hadith. Hence they have ruled that one should not say it.