Does intending to fulfill a vow of fasting one month by fasting the month of Ramadan suffice?

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The vow is not fulfilled by fasting the month of Ramadan if the intention includes fulfilling the obligation of Ramadan itself. This is because the obligation of fasting Ramadan is established by God's decree, and the vow requires the obligation of an entire month, resulting in two obligations. One cannot discharge the other. This is analogous to vowing to fast two months or vowing to pray two rak'ahs, where the obligatory Fajr prayer does not discharge the vow, nor does the vow discharge the Fajr prayer. This is supported by the principle that if two distinct obligations arise from two causes, they must both be fulfilled.