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Replacement effects, such as a permanent entering the battlefield tapped or with counters on it, are unaffected. Abilities that apply "as [this permanent] enters the battlefield" are replacement effects.

Look at the permanent as it exists on the battlefield, taking into account continuous effects, to determine whether any triggered abilities will trigger. For example, if you control Opalescence, which says, in part, "Each other non-Aura enchantment is a creature," each enchantment will be a creature at the time it enters the battlefield and will not cause triggered abilities to trigger.

If Doorkeeper Thrull and another creature or an artifact enter the battlefield at the same time, neither one will cause triggered abilities to trigger when they enter the battlefield.

The trigger event doesn't have to specify artifacts or creatures entering the battlefield. For example, Tireless Tracker has an ability that says "Whenever a land enters the battlefield under your control, investigate." If an artifact land or creature land enters the battlefield under your control, that ability won't trigger. If a nonartifact, noncreature land enters the battlefield under your control, the ability will trigger.

Triggered abilities use the word "when," "whenever," or "at." They're often written as "[Trigger condition], [effect]." Some keyword abilities are triggered abilities and will have "when," "whenever," or "at the beginning of" in their reminder text.