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Does anyone know if "Feel no Pain" from Disgusting Resilient or Psychic ability or Warlord Trait,

Can they be used to avoid Mortal Wound from Smite? Peril of the Warp? Vehicle Explode?

Yes. FnP mechanics is not a save mechanism, but a wound mitigation mechanism.

However, you roll separately for any wounds cause by multi damage weapons individually.

It does not, however, affect "slain" or "removed from play" mechanics.

darrekbaal wrote:
Does anyone know if "Feel no Pain" from Disgusting Resilient or Psychic ability or Warlord Trait,

Can they be used to avoid Mortal Wound from Smite? Peril of the Warp? Vehicle Explode?

Yes. Feel No Pain style abilities work fine on mortal wounds.

And just to really lock it in, the Rulebook FAQ answers this:

Q: Can abilities such as Disgustingly Resilient be used to ignore wounds if they were inflicted by mortal wounds?
A: Yes.

Ghaz keeps an updated list of FAQs here, which also has the link to the official FAQ page https://www.dakkadakka.com/dakkaforum/posts/list/736188.page