Does the prayer become void for someone who intended to say the Tasleem, then remembered a supplication and supplicated with it, and then said the Tasleem?

The Taslim (concluding salutation) of prayer is a pillar, and one cannot exit the prayer without it. By it, the worshiper intends to exit the prayer, salute the Imam and those with him, and the guardian angels. If the worshiper intends the Taslim, then remembers a supplication and recites it, and then performs the Taslim, their prayer is valid. This is because this intention is not a severance of the prayer. As long as they have not performed the Taslim and have not intended to exit, they are still continuing their prayer. Therefore, what the person did is permissible, and their prayer is valid.