The Shulhan Aruch (Orah Haim 548; listen to audio recording for precise citation) rules that if a person completed the seven-day Shiba observance after the death of a family member, and Yom Tob begins during the thirty-day period of Sheloshim, once Yom Tob begins he no longer needs to observe Sheloshim. As long as the Shiba period has been completed before the onset of the Yom Tob, the Yom Tob "cancels" the Sheloshim observance, and the restrictions no longer apply. The Shulhan Aruch adds that even if the seventh and final day of Shiba is Ereb Yom Tob, the mourner is permitted to take a haircut and shave on that day, since the imminent onset of Yom Tob cancels the Sheloshim restrictions.
However, later in this chapter (Seif 9), the Shulhan Aruch notes that this rule does not apply to a person mourning the passing of a parent. The laws of Abelut are generally more stringent in the case of a parents death, and in this instance the onset of Yom Tob does not end the Sheloshim observance for a father or mother. Even though the mourner completed the Shiba observance before the onset of Yom Tob, he must observe the full Sheloshim period, unless he is mourning the death of a family member other than a father or mother.
Summary: If a mourner completed the Shiba observance before the onset of Yom Tob, then the onset of Yom Tob "cancels" the remainder of the thirty-day restrictions of Sheloshim, except if one mourns the loss of a parent, in which case he must observe Sheloshim even in such a case.
