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Not knowing the details, I'd say that generally speaking, your plan is fine.
Closed cards will typically remain on your report for up to 10 years or even more in some cases. Sometimes, they do drop off sooner, but that's relatively rare. In short, expect your account age stats to be unaffected in the short term. Longer term, if your oldest card is a lot older than your other cards, you might want to keep it around.
Having three open cards is good for scoring purposes, and some say that five is better. Your plan has you hitting both of those marks.