If one prays the pre-Fajr sunnah in the mosque, is he required to pray the greeting of the mosque?

Question:
Honorable Shaykh, may Allah grant you success, what is the ruling on praying the rawatib before Fajr, and likewise the greeting of the mosque, if one prays four rak'ahs before Fajr? Is this action valid?

Answer:
No, he prays the rawatib of Fajr, and that suffices for the greeting of the mosque. He prays the rawatib of Fajr, two rak'ahs, and that suffices for the greeting of the mosque; he enters into it. Yes.