Does praying Tahiyyat al-Masjid mean that one does not have to pray Sunnat al-Fajr?

If a person enters the mosque and prays Tahiyyat al-Masjid, does that mean that he does not need to pray the two Rak’ahs of Sunnat al-Fajr? Or should he pray Tahiyyat al-Masjid and then do the two Rak’ahs of Sunnat al-Fajr?

Praise be to Allah, and blessings and peace be upon the Messenger of Allah:

If he enters the mosque and prays Sunnat al-Fajr, this is sufficient and he does not have to pray Tahiyyat al-Masjid. If he makes the intention of praying both, then that is fine.

And Allaah is the source of strength. May Allaah bless our Prophet Muhammad and his family and companions.