Hi, I am remodeling my kitchen and worked myself into a bit of trouble. I realize this was my own dumb mistake, but I wanted to check what I think is a solution.

While remodeling, I installed a deeper sink, which dropped my garbage disposer a couple inches. The disposer outflow is now below the sink drain pipe which runs into the wall. Based on everything I know about gravity and plumbing, this won't work out.

There is an older, capped drain pipe (six inches lower) behind the dishwasher which also runs into the wall; it ties into the wall pipe in the wall with a wye. Is there any reason I shouldn't run my sink pipes to the lower drain pipe and cap the one I was using before? Then, everything would run downhill, and all the water should still end up in the same place. I think this should work, but would like some reassurance from somebody with more experience.

Thanks for the help!