When I had a Tamer with [Izzy Izumi] in its name, I used this card to give 1 of my opponent's Digimon "[On Deletion] Trash the top card of your security stack." If I later lose my Tamer with [Izzy Izumi] in its name, will my opponent's Digimon no longer be affected by that effect?
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Official Ruling
No. As long as the conditions were met at the time you activated the effect, the effect will persist and will last until the end of your opponent’s turn, even if the conditions are no longer met at a later point.
