Can Brynhir Thundersong's trigger be responded to after he enters?

After Brynhir Thundersong hits the field, his "When you play me, opponents can't play cards this turn" trigger goes on the chain. Can opponents respond to it, and does killing him prevent the trigger from resolving?

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•Riftbound Community Server — Rules Questions

TimingTrigger

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Can Brynhir Thundersong's trigger be responded to after he enters?

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