JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
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It is not possible to add a date to the "Limit Dates" list based on a submission. If you want to disable a date once a user has already reserved it, you can use the Date Reservation Widget instead of the date field. This widget will automatically disable the date if they have previously been selected by another user before.
Here's a demo form so you can see it in action: https://form.jotform.com/61475511548963