Let's say a miniature has both the Feel No Pain and Eternal Warrior rules. It is wounded by a weapon that inflicts Instant Death. Is it allowed to use the Feel No Pain rule to try to negate the wound?

Snippets from relevant rules :
Eternal Warrior (p. 35): "A model with this special rule is immune to the effects of Instant Death."
FNP(p. 35): ..."Note that Feel No Pain rolls cannot be made against unsaved Wounds that inflict Instant Death."...
Instant Death (p. 38): "Unsaved Wounds inflicted by an attack with this special rule automatically inflict Instant Death."... (p. 16) ..."...it is reduced to 0 Wounds and removed as a casualty."...