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This is terrible.
Irelia is not a right-click champion, she relies on her spell combo to deal damage.
You rely on a short duration active with a long cooldown, but you don't get any cd.
There is also little survivability in there other than the BV, which is a pretty standard item for any champ. Personally I believe all melee champs should build some survivability, with a few exceptions.
Irelia isn't even a carry anyways, she's a tanky anti-carry.