Due to this card's effect, the DP on one of my opponent's Digimon becomes 0.At this point in time, is that Digimon with 0 DP immediately deleted?
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No, it is not immediately deleted at this point in time.All activated effects are resolved, after which a rule check occurs. At that point in time, all Digimon with 0 DP are deleted simultaneously.
Source: EX13-060 Alphamon