I've traveled all over the United States with no issues. I've even visited Alaska and Hawaii. I am going to Puerto Rico soon.
Just use your State ID and if you want, make a copy of your EAD and leave it in your wallet. I've had no reason to bust it out, but have it just in case.
Where you looking to go?
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5th EAD
Sent to Phoenix Lockbox:
12/14/19
Received:
12/16/19
Biometrics/Approved:
TBD
Expiring:
05/14/20