When this card would leave the battle area other than by my effects, I try using its [All Turns] effect to delete another Digimon but another effect prevents it.At this time, does this card not leave the battle area?
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No, it leaves the battle area.If the "by doing X" condition isn't met, the rest of the effect isn't processed.In this case, this card leaves the battle area if the deletion isn't possible.
Source: EX13-015 Gallantmon