Is it obligatory to repeat the Fajr prayer if the worshiper doubts whether he said the Tasleem between the Fard and Sunnah or not?

If a worshipper doubts having performed the taslim (salutation) in a supererogatory prayer, or the takbirat al-ihram (opening glorification) in a fard (obligatory) prayer, and a long interval has passed, the prayer is invalidated in both cases and must be repeated. This is because doubt concerning a pillar (rukn) is like abandoning it. As for the person afflicted with obsessive doubts (al-muswas), they should not pay attention to their doubts.