If I put a SIM card into an unlocked iPhone will it lock it to that phone?

I recently received an unlocked iPhone 5s as a replacement from LifeProof.
The point is, it says ATT unlocked. It says SIM required when I turn on the phone. I have a sim card but it's from my current service which I'm going to cancel so I don't know if there's a way to bypass the sim required. Or if I use my current sim card will I no longer be able to use another one?

If the phone is unlocked, you can use any SIM from any GSM carrier.