Rule 614.8 · Replacement Effects

Regeneration is a destruction-replacement effect. The word “instead” doesn’t appear on the card but is implicit in the definition of regeneration. “Regenerate [permanent]” means “The next time [permanent] would be destroyed this turn, instead remove all damage marked on it and its controller taps it. If it’s an attacking or blocking creature, remove it from combat.” Abilities that trigger from damage being dealt still trigger even if the permanent regenerates. See rule 701.19.