What allows Irelia to build full tank and still do so much damage?

If she doesn't have any damage items she won't be doing damage.

Yes, Triforce is a damage item.

Botrk+TF then tank allows her to shred almost anyone.

If your getting stomped by a full tank Irelia, the problem is you, not her.

Trinity procs and 75 True Damage OnHit are no joke.

It's not just the true damage, it's trinity force. It synergizes perfectly with her kit. Attack speed for true damage, crit chance, sheen procs. Not to mention any other on hit effects she gets from items (botrk, wit's end, etc).

Also, when you see an Irelia doing crazy damage it's usually during mid game and against squishies (ADCs and APCs) who honestly can die just from being looked at.

I have never seen an Irelia build full tank. Are you sure they didn't have Trinity Force and maybe another damage item (Blade of the Ruined King, Ravenous Hydra, Zephyr)?

Anyways, most Irelia players I see have two damage items and three tank items. In addition, Irelia players usually build a lot of CDR so they can use their abilities more often. In addition, Irelia has good base damage against squishy champions and a lot of synergy with spellblade items.

Dat trinity + heart + visage + ghostblade 40% cdr op!

Irelia doesn't even go full tank, she get's tri force for her main damage and gets some tanky item afterwards. And you only need 1 damage item to kill squishies.

How are you losing to full tank Irelia

The true damage is a pretty big part of it, yes. At 75 True Damage on hit at level 9, she can hurt tons. She also has the potential to have 6 Sheen procs because of her ult (as opposed to 4 most other champions get) But I've yet to see an Irelia build full tank. I'd imagine it'd be fun though, having tons of armor, health, MR AND tenacity. You could literally run in and out of the enemy team, and laugh it off.