Yes. Magic items in the DMG refer to mundane items listed in the PHB, and use the corresponding stats. Staffs, rods, and wands are listed in the PHB as categories of Arcane Foci, therefore anything listed as one of these types of items in the DMG is referring to an Arcane focus.

If you were to assume that items in the DMG do not correspond to the stats listed for them in the PHB unless explicitly stated, you would have to assume that all armor, shields, and weapons in the DMG have ambiguous stats. That would mean that all of these items are not actually armor or weapons unless explicitly stated, which is absurd.

Some items are explicitly listed as arcane foci, such as the Tome of the Stilled Tongue. This is because they are an item type that is not listed in the PHB as an arcane focus.

Yes. Magic items in the DMG refer to mundane items listed in the PHB, and use the corresponding stats. Staffs, rods, and wands are listed in the PHB as categories of Arcane Foci, therefore anything listed as one of these types of items in the DMG is referring to an Arcane focus unless otherwise stated.

If you were to assume that items in the DMG do not correspond to the stats listed for them in the PHB unless explicitly stated, you would have to assume that all armor, shields, and weapons in the DMG have ambiguous stats. That would mean that all of these items are not actually armor or weapons unless explicitly stated, which is absurd.

Some items are explicitly listed as arcane foci, such as the Tome of the Stilled Tongue. This is because they are an item type that is not listed in the PHB as an arcane focus.

Yes. Magic items in the DMG refer to mundane items listed in the PHB, and use the corresponding stats. Staffs, rods, and wands are listed in the PHB as categories of Arcane Foci, therefore anything listed as one of these types of items in the DMG is referring to an Arcane focus.

If you were to assume that items in the DMG do not correspond to the stats listed for them in the PHB unless explicitly stated, you would have to assume that all armor, shields, and weapons in the DMG have ambiguous stats. That would mean that all of these items are not actually armor or weapons unless explicitly stated, which is absurd.

Yes. Magic items in the DMG refer to mundane items listed in the PHB, and use the corresponding stats. Staffs, rods, and wands are listed in the PHB as categories of Arcane Foci, therefore anything listed as one of these types of items in the DMG is referring to an Arcane focus.

If you were to assume that items in the DMG do not correspond to the stats listed for them in the PHB unless explicitly stated, you would have to assume that all armor, shields, and weapons in the DMG have ambiguous stats. That would mean that all of these items are not actually armor or weapons unless explicitly stated, which is absurd.

Some items are explicitly listed as arcane foci, such as the Tome of the Stilled Tongue. This is because they are an item type that is not listed in the PHB as an arcane focus.