If Brynhir Thundersong is played and the opponent responds with Shakedown (destroying Brynhir), does the 'can't play cards this turn' effect still apply?

Ruling: Yes, the effect still applies. The trigger goes on the chain when Brynhir enters and becomes independent from that point on. Removing Brynhir has no impact on the trigger.

Nuances:

• The trigger is a separate entity once it goes on the chain
• Removing the source of a trigger does not cancel the trigger that has already been placed on the chain