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Nashor's Tooth
The reason this item is essential for this build is because it gives both ap and attack speed, whilst giving an on hit effect that scales with ap.

Guinsoo's Rageblade
This item grants attack speed that increases with each attack up to 6 times. The item also gives % magic penetration and ap, two things teemo can use.

Liandry's Torment
This item gives increased damage for each second in combat, good for team fights. The item also grants a burn on champions hit with abilities (increasing by 1% on movement impaired champions), making your poison even more potent.

Mejai's Soulstealer
This item AKA the book of getting kills grants ap normaly, but should not be bought unless you are above 10 stacks. The bonus ap and MS from ten stacks makes you even more of a monster. Sell if you ever drop below 10 stacks.

Morellonomicon
This item grants ap, grievous wounds(turns off healing for champions damaged), and magic penetration.

Twin Shadows
The item's stats grant CDR, AP, and MS, all good things for teemo. The active is the really good part for this build. When activated two ghosts go out and slow a near by enemy, which means you can run them down and auto attack them.

Rabadon's Deathcap
AAAPPPPPPP