If I have a factory unlocked iphone 4, can I upgrade it to ios 6?

My iphone was unlocked online from it's original provider that was European, now I use it with t-mobile in usa. Had to get it unlocked after updating to 5.1.1 which updated to new firmware, which made my gevey sim useless. Is it possible to update/upgrade? I don't want it to get locked again.

Added (1). Thank you so much

If it is Factory Unlocked, not a Jailbreak so yes you can upgrade to it to iOS 6.it will not locked again.

Yes you can if it is factory unlocked.

With a factory unlock you can update.
After we unlock your iphone http://attiphoneunlocker.com/ connect to itunes with a non accepted sim (for example a tmobile sim) and do a back up and restore. Your phone can now be used with any gsm network. You can safely update the OS on your handset at any time, and sync your device with your computer without fear of Apple removing your unlock
We provide an AT&T Official, Permanent, Apple unlock that remove any network restrictions your iPhone may have by marking your handset as unlocked in Apple's IMEI database.
Once your Unlock has been processed just follow these simple steps:

1) Open iTunes on your Mac or PC (verify you have internet connectivity).

2) Connect your iPhone to your computer using the USB data cable.

3) Backup and Restore your iPhone using iTunes.

4) Once your iPhone is restored it will have the Factory Unlock in place!

http://attiphoneunlocker.com/

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