I went in a couple times when I had one shot, and they let me in - you should be fine. For the exemption letter, because it’s a city mandate and not Regal’s, you would have a harder time with that, but still worth a try!
You must show a copy of the card with a photo id. I carry a picture on my phone. You can also show proof of negative result provided it's done a day before show.
You just need to show your Vax card along with photo ID. One or both shots is fine.
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