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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.

Phasing out doesn't cause any "leaves the battlefield" abilities to trigger. Similarly, phasing in won't cause any "enters the battlefield" abilities to trigger.

As Blink Dog phases out, Auras and Equipment attached to it also phase out at the same time. Those Auras and Equipment will phase in at the same time Blink Dog does, and they'll phase in still attached to Blink Dog.

Phased out permanents are treated as though they don't exist. They can't be the target of spells or abilities, their static abilities have no effect on the game, their triggered abilities can't trigger, they can't attack or block, and so on.

Permanents phase back in during their controller's untap step, immediately before that player untaps their permanents. Creatures that phase in this way are able to attack and pay a cost of {T} during that turn. If a permanent had counters on it when it phased out, it will have those counters when it phases back in.

An attacking or blocking creature that phases out is removed from combat.

Any continuous effects with a "for as long as" duration, such as that of Mind Flayer, ignore phased-out objects. If ignoring those objects causes the effect's conditions to no longer be met, the duration will expire.

Choices made for permanents as they entered the battlefield are remembered when they phase in.

If an opponent gains control of your Blink Dog, activates its Teleport ability, and the duration of the control-change effect expires before it phases in, Blink Dog phases in under your control as that opponent's next untap step begins. If they leave the game before their next untap step, Blink Dog phases in as the next untap step begins after their turn would have begun.