Is establishing the prayer, when making up a missed obligatory prayer, a condition for its validity?

The Adhan and Iqama for a missed prayer are Sunnah (recommended) and not obligatory according to the four Imams. It is good to perform both or to suffice with the Iqama, and the validity of the prayer does not depend on them. However, if there are multiple missed prayers, the Adhan should be called for the first one, and the Iqama should be made for each subsequent prayer. The legality of calling the Adhan for a missed prayer is mentioned in the Hadith of the Battle of the Trench. As for the Adhan and Iqama for a prayer performed on time, there is disagreement regarding their obligation, but they are not a condition for the validity of the prayer.