If I am travelling to US from Aus for example on Saturday morning, zuhr of Saturday will occur while on plane. Now when I land in US, it is still Saturday morning there and Zuhr of Saturday will occur a second time for me. Now please guide me which Zuhr to pray and which one to leave or pray both? What will be the niyyat in both cases?

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When you have done Namaz Zuhr then the wajib has been done. It is mustahab to repeat it again if you reach when you arrive at your destination.