Is it permissible to pray the two rak'ahs of "Tahiyat al-Masjid" (Greeting the Mosque) after performing the Sunnah of Fajr at home and intending to go to the mosque to pray Fajr?

It is sunnah for whoever enters the mosque to pray two rak'ahs before sitting, according to the Prophet's saying, "When any one of you enters the mosque, he should not sit until he prays two rak'ahs." If he sits before praying, it is sunnah for him to stand up and pray them. And if he prays the regular sunnah prayer upon entering the mosque, it suffices for the salutation of the mosque (tahiyyat al-masjid), because the intention is to perform two rak'ahs before sitting.