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Anivia has a number of great things about her.
q aoe nuke that stuns possible double hits.
w anti initiation/initiation..box out everyone that will followup
e heavy heavy nuke if frosted
r heavy pushing easy application of frost huge zone control attack speed reduction low cd.
Base stats..not anywhere near the worst
passive lol you just bursted me...ok i'm up again..
So to beat her you need high sustained damage high pushing ability and being able to survive burst...
on top of that you need to deal with her teamfight strength so she doesn't capatalize on that..The only thing that comes to mind is a sivir with full ad marks and quint. Its been a while since i've seen sivir mid but it can still be done. Cho can also challenge her.. she frosts you, counter with w push back with e knockup and naturally tanky. True damage won't matter vs her runes.