I took 2 from the Gifted Aetherborn.
He gained 2 from the Aetherborn's Lifelink.
My question is: Do I lose another life from the Vampire even though it was killed in battle? How does the timing work for triggered abilities during the cleanup phase and how is priority determined?
Yes, you lose another life. The way this works is this (note that there are a few priority passes I am skipping over):
Attackers are Declared.
Blockers are Declared.
Combat Damage is dealt. Gifted Aetherborn deals 2 damage. Its controller gains two life.
Simultaneously, the Cliffhaven Vampire deals 2 damage to the creature blocking it and is dealt at least 4 damage.
Because life is gained, Cliffhaven triggers.
Before that trigger goes onto the stack, State-Based Actions are checked and sees a Cliffhaven Vampire with lethal damage on it. The Vampire is destroyed.
The Vampire's trigger goes onto the stack and the Active Player gets priority.
Priority is passed by both players and you lose 1 life when the ability resolves.
Note the important part is that the trigger condition (gaining life) is met while the Vampire is still on the battlefield. A phrase I like (and have seen a couple of places): Damage doesn't kill creatures; State-Based Actions do. Since the creature hadn't been destroyed yet, it still saw the life gain event.
The Cleanup Step is the last step of the turn, it doesn't happen during combat. The relevant step here is the Combat Damage Step.
Assuming the creature that blocked Cliffhaven Vampire didn't had First Strike or Double Strike:
As the Combat Damage Step begins, players determine how their creatures will deal combat damage - his Gifted Aetherborn deals 2 damage to you (and, because it has Lifelink, your son also gains 2 life at the same time), Cliffhaven Vampire deals 2 damage to the creature that blocked it, and your blocker deals 4+ damage to the Cliffhaven Vampire. All this damage is dealt simultaneously (and so is the life gain); the Cliffhaven's hability triggers from the life your son gained at this point.
Then, the Cliffhaven is destroyed by the lethal damage from the blocker, going to the graveyard.
Then, the Cliffhaven's triggered ability goes to the stack.
Then, the active player (your son, as it is his turn) gains priority. Assuming both him and you pass, the Cliffhaven's ability resolves, making you lose 1 life.
Cliffhaven Vampire doesn't die until after damage is dealt.
Damage being dealt causes your opponent to gain life.
Cliffhaven Vampire triggers when your opponent gains life.
Therefore the Vampire doesn't die until after its ability triggered.
Your reference to cleanup is spurious, as willdice notes. Priority is also spurious, since it determines only who may initiate actions, whereas the bulk of your scenario plays out automatically.
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Do note that this answer (you loosing one life) is only possible because Gifted Aetherborn has Lifelink (which gives life simultaneously with the damage being dealt); things would be different if he attacked you with, say Horned Cheetah, which has a triggered 'pseudo-lifelink' ability. In this case, Cliffhaven Vampire would not have had time to trigger.
He attacked with Gifted Aetherborn and Cliffhaven Vampire. I blocked and killed the Cliffhaven Vampire.
I took 2 from the Gifted Aetherborn.
He gained 2 from the Aetherborn's Lifelink.
My question is: Do I lose another life from the Vampire even though it was killed in battle? How does the timing work for triggered abilities during the cleanup phase and how is priority determined?
Blockers are Declared.
Combat Damage is dealt. Gifted Aetherborn deals 2 damage. Its controller gains two life.
Simultaneously, the Cliffhaven Vampire deals 2 damage to the creature blocking it and is dealt at least 4 damage.
Because life is gained, Cliffhaven triggers.
Before that trigger goes onto the stack, State-Based Actions are checked and sees a Cliffhaven Vampire with lethal damage on it. The Vampire is destroyed.
The Vampire's trigger goes onto the stack and the Active Player gets priority.
Priority is passed by both players and you lose 1 life when the ability resolves.
Note the important part is that the trigger condition (gaining life) is met while the Vampire is still on the battlefield. A phrase I like (and have seen a couple of places): Damage doesn't kill creatures; State-Based Actions do. Since the creature hadn't been destroyed yet, it still saw the life gain event.
Assuming the creature that blocked Cliffhaven Vampire didn't had First Strike or Double Strike:
As the Combat Damage Step begins, players determine how their creatures will deal combat damage - his Gifted Aetherborn deals 2 damage to you (and, because it has Lifelink, your son also gains 2 life at the same time), Cliffhaven Vampire deals 2 damage to the creature that blocked it, and your blocker deals 4+ damage to the Cliffhaven Vampire. All this damage is dealt simultaneously (and so is the life gain); the Cliffhaven's hability triggers from the life your son gained at this point.
Then, the Cliffhaven is destroyed by the lethal damage from the blocker, going to the graveyard.
Then, the Cliffhaven's triggered ability goes to the stack.
Then, the active player (your son, as it is his turn) gains priority. Assuming both him and you pass, the Cliffhaven's ability resolves, making you lose 1 life.
Damage being dealt causes your opponent to gain life.
Cliffhaven Vampire triggers when your opponent gains life.
Therefore the Vampire doesn't die until after its ability triggered.
Your reference to cleanup is spurious, as willdice notes. Priority is also spurious, since it determines only who may initiate actions, whereas the bulk of your scenario plays out automatically.
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