Enchantment still trigger ability when it destroy
- Enchantment trigger ability
- System trigger resolve action
- Use instant to destroy the enchantment
Result:
The enchantment destroyed but it still trigger the ability
Expect:
The enchantment destroyed but it WILL NOT trigger the ability

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Rezzahan#77802 commented
You cannot stop a trigger by removing its source after it already triggered. That's Magic 101, the utmost basics. You need to learn the rules of this game.
113.7a Once activated or triggered, an ability exists on the stack independently of its source.
Destruction or removal of the source after that time won’t affect the ability. Note that some
abilities cause a source to do something (for example, “Prodigal Pyromancer deals 1 damage to
any target”) rather than the ability doing anything directly. In these cases, any activated or
triggered ability that references information about the source for use while announcing an
activated ability or putting a triggered ability on the stack checks that information when the
ability is put onto the stack. Otherwise, it will check that information when it resolves. In both
instances, if the source is no longer in the zone it’s expected to be in at that time, its last known
information is used. The source can still perform the action even though it no longer exists.