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If I give my 1/1 creatures +3/+3 in response to my opponent getting Demon of Dark Schemes out, then my opponent cast Blasphemous Act and I give my creatures indestructible. Will my creatures live or will they die?

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They live.

Damage doesn't change its toughness, it's "marked" on a creature. See 120.5 - when state-based actions are checked, that's how and when the creature would be destroyed by lethal damage.

so the way it sounds like this happens:

  1. you have some 1/1s
  2. your opponent casts Demon of Dark Schemes
  3. in response, while Demon of Dark Schemes is on the stack, you do something to give your creatures +3/+3.
  4. no response from anyone. +3/+3 resolves, your 1/1s are 4/4s
  5. no response from anyone. Demon of Dark Schemes resolves. Your 4/4s are now 2/2
  6. your opponent casts Blasphemous Act
  7. in response, you give your creatures indestructible until end of turn
  8. no response from anyone, your creatures are indestructible
  9. no response from anyone, Blasphemous Act resolves; 13 damage is dealt to your 2/2 indestructibles
  10. before the next player gets priority, damage is checked as a state-based action. your 2/2s are indestructible, they ignore this check (see 702.12b).
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    Importantly also, all these effects end "at the same time" (i.e. without SBAs being checked in-between) at the end step.
    – Caleth
    Jun 1 at 9:38

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