Shifting the intention from one obligatory prayer to another.

Question:
I missed the Fajr prayer on Friday, and I did not wake up from sleep until before the Jumu'ah prayer. So I hurried to the Jumu'ah prayer and said the opening takbir with the imam. Then I remembered that I had not prayed Fajr, so I intended that it be Fajr. Is my action valid?

Answer:
Answer: No. They say: If one shifts his intention from one obligatory prayer to another, both are invalid; the one he shifted to and the one he shifted from are invalid. One does not shift his intention from one obligatory prayer to another during the prayer.