How to downgrade my iphone 4 to ios 6?

I have an iphone 4 (Verizon) with ios 6 i connected it with itunes and made a backup, then i connected my other iphone 4 (AT&T) ios 7.0 and clicked on the restore button from itunes. If i restore it with the backup point i made with the verizon device would it downgrade to ios 6 or completely mess up everything?

A restore does not revert back to a previous iOS.