Q: will i lose ringtones bought on my iphone if i sync it to a new itunes library on my new computer

I am trying to put music on my new iphone. however when I go to sync it a message pops up saying my account is synced to a different iTunes library. it gives me the option to erase my old iTunes library and replace it with my new one.

I am ok to do this because I don't have anything from my old iTunes library on my new phone but I have bought two ringtones from the iTunes on my phone. Will I lose those ringtones if I sync to my new iTunes?