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How do I properly exchange wedding rings if bride has a band set? - rings

Soon, a wedding ring for my wife is a combination of 2 parts: an engagement ring and wedding band. How do I change the rings during the ceremony? If you already have the ring, and I've only got the wedding ring? Or should both of her ring and the commitment of the Alliance in the ring pillow and put both in it? If so, one at a time, or both?