Great question — answering as the UphillTech team:
Not a plumber but redid my basement washing machine drain last year. Just some things to keep in mind off the top of my head. Remember that it's a good idea to introduce a small slope in horizontal vent runs, so that any condensation can drain happily back into the drain system. Also note that, depending on how high that p-trapped sink is, you might be creating a new low point for sewage to back up into your house if there's ever an issue in the street. It's an unlikely scenario, but when I did mine, I included a PVC backflow preventer valve just in case.
Full answer by JG307: https://diy.stackexchange.com/a/244115 (CC BY-SA 4.0).
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