If a 'dies' trigger and a 'leaves the battlefield' trigger are on the same creature, do both fire when it dies?

When a creature dies (is put into the graveyard from the battlefield), it has simultaneously satisfied two different trigger conditions: a 'dies' trigger (which watches for the permanent going to the graveyard from the battlefield) and a 'leaves the battlefield' trigger (which watches for the permanent leaving the battlefield for any zone). Both are checked at the same moment the event occurs.

Under CR 603.2, triggered abilities trigger at the moment their trigger event occurs. Since dying is a specific case of leaving the battlefield, both trigger conditions are met by the same event. Neither one 'uses up' the event — each trigger is evaluated independently against what just happened.

Both triggered abilities are placed on the stack at the same time (CR 603.3b). If the same player controls both, that player chooses the order they are placed on the stack, meaning the last one placed will resolve first. If different players control them, APNAP order (Active Player, Non-Active Player) applies.

Example: You control a creature enchanted with an aura that has a 'leaves the battlefield' trigger, and the creature itself has a 'dies' trigger. When the creature dies, both the creature's own dies trigger AND the aura's leaves-the-battlefield trigger fire simultaneously and are placed on the stack.

Relevant rules: CR 603.2 (when triggered abilities trigger), CR 603.3b (multiple triggers going on the stack), and the definition of 'dies' in CR 700.4 (a permanent 'dies' if it is put into the graveyard from the battlefield).