Who will appear first, Imam Mahdi or Dajjal? What will be the sequence of events?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

According to the sound Ahadith "Imam al-Mahdi will appear before Dajjal (Antichrist).  When the Muslim conquests reach Constantinople, Satan will yell loudly: “Dajjal has reached your families” as reported in Saheeh Muslim.

Dajjal (antichrist) will remain in this world for forty days and after that Prophet (Sallallahu Alaihi wa Sallam) I'sa (Jesus) will descend and kill the Antichrist.  It is reported in Sound Ahadith that the Prophet I'sa will offer the prayers behind al-Mahdi. 

The above details are narrated in Saheeh Muslim and other books of Sunan.

There is no sound Hadith that proves the sequence of all the events that will happen.  However, there are some Ahadith that prove the sequence of some events such as the appearance of Antichrist, descent of Prophet I'sa (Alaihi As-Salaam) appearance of Yajug Maju’j (gog and magog), and the last sign of the Hour, i.e. the sun rising from the west.  All of the above major Signs of the Hour have not appeared yet.

Allah knows best.