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If an ability would produce one or more mana of an undefined type, it produces no mana instead.

Some abilities produce mana based on the type of mana another permanent or permanents “could produce.” The type of mana a permanent could produce at any time includes any type of mana that an ability of that permanent would produce if the ability were to resolve at that time, taking into account any applicable replacement effects in any possible order. Ignore whether any costs of the ability could or could not be paid. If that permanent wouldn’t produce any mana under these conditions, or no type of mana can be defined this way, there’s no type of mana it could produce.

To “tap [a permanent] for mana” is to activate a mana ability of that permanent that includes the {T} symbol in its activation cost. See rule 605, “Mana Abilities.”

An ability that triggers whenever a permanent “is tapped for mana” or is tapped for mana of a specified type triggers whenever such a mana ability resolves and produces mana or the specified type of mana.

A replacement effect that applies if a permanent “is tapped for mana” or tapped for mana of a specific type and/or amount modifies the mana production event while such an ability is resolving and producing mana or the specified type and/or amount of mana.

If an object’s enters-the-battlefield triggered ability or replacement effect refers to X, and the spell that became that object as it resolved had a value of X chosen for any of its costs, the value of X for that ability is the same as the value of X for that spell, although the value of X for that permanent is 0. This is an exception to rule 107.3i.

The tap symbol is {T}. The tap symbol in an activation cost means “Tap this permanent.” A permanent that’s already tapped can’t be tapped again to pay the cost. A creature’s activated ability with the tap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

The untap symbol is {Q}. The untap symbol in an activation cost means “Untap this permanent.” A permanent that’s already untapped can’t be untapped again to pay the cost. A creature’s activated ability with the untap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

Angelic Arbiter's last ability applies if an opponent attacked with at least one creature during the current turn.

If Angelic Arbiter enters during an opponent's turn, its abilities take actions that player performed earlier in the turn into account, even though it wasn't on the battlefield at the time. For example, if an opponent casts a spell, then you use Leyline of Anticipation's ability to cast Angelic Arbiter as though it had flash, that player won't be able to attack with creatures that turn.

During your turn, Angelic Arbiter's abilities have no effect on the game.

If Angelic Arbiter leaves the battlefield during an opponent's turn, its abilities cease to affect the game. For example, if an opponent casts Doom Blade to destroy Angelic Arbiter, that player may then attack with creatures.

During an opponent's turn, that opponent may either cast spells or attack with creatures, but not both (assuming that Angelic Arbiter is on the battlefield for the entirety of that turn). The player may perform other actions, such as activating abilities and playing lands.