Can i sync 1 iphone to two different itunes?

I got a new computer and I had an itunes on my old one and I want to use my new computers itunes but the problem is i also used my ipod on my new computer so i'm scared if I download songs and such it will delete everything on my phone or old itunes. Because i tried to download some songs and a pop up showed up saying if i sync it it will erase my iphones stuff and replace it with my other apple device!

Just copy all your songs/apps off your old machine to your new one and import into iTunes.

Authorize you new computer to play your ITunes music

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