Can I use my Iphone with any carrier after a jailbreak?

Originally i bought my iphone from a guy said it was jailbroken. I activated the phone to At&T. The phone was messing up after awhile so i downloaded IOS 6.0.1. Surprisingly my service still worked. It seems like its not jailbroken anymore? I want to activate on a Verizon line but i don't know if I have to jail break it again?

No, it has to be unlocked, and unlocking it will only allow you to take it to different GSM networks.AT&T will unlock iPhones that aren't on contract after a certain amount of time.

Verizon is a CDMA network. You will never be able to activate an AT&T iPhone on Verizon, even though the 4S and 5 have both GSM and CDMA bands, the CDMA portion is unusable on GSM models.