All perfect praise be to Allaah, the Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
Fasting the first nine days of Thul-Hijjah is, of course, a legitimate act of worship. However, as far as we know, there is not even a single Hadeeth, neither Saheeh nor Hasan nor Dha‘eef, indicating that the reward of fasting them equals the reward of performing Hajj.
Fasting each of these days is an independent act of worship; hence the validity of fasting each day thereof is not contingent on fasting the other days. Rather, the person is rewarded according to the number of days he fasts.
Allaah Knows best.