no, all you need is a light sanding. If you used that much tsp I hope you rinsed ,rinsed, rinsed, rinsed, rinsed, and then rinsed, again

The cabinets will be more durable if you sand them down to raw wood. This is because the primer will stick best to raw then to some slick old finish, plus the primer can penetrate raw wood. It can't penetrate if you are painting over varnish or some other shiny surface. Personally, I think that if you are planning to sand your cabinets down to raw, then there is no need to clean them at all because you will be sanding through whatever you cleaned, it's a waste of time. It's not necessary to completely strip your cabinets though in order to paint them. Primers and paints are pretty good these days that you can still make them pretty durable by just painting over the finish. It just depends on how particular you are and how far you want to take the project.

Chris and paintguy, thank you very much for your help.