Cabinet with angle from front to back

I am trying to design a cabinet with a 45 deg angle at the top that runs front to back. I created the cube with a recessed 3/4" inset and tried a couple of different methods using the protractor and line tools to create the angle. I tried using the protractor on the interior and exterior of the cabinet, and the line tool on the outside of the cabinet to then push away the waste, but I keep getting the same result or some variation of it. From the image you can see that it’s not removing all of the structure. It’s creating an object that isn’t solid.

Tap the Option/Alt key after you start the push pull operation to continue past the first stopping point.

Then select successive faces to remove the remaining parts you want to trim off at 45°.

I think I would draw the section profile first, then push-pull to extrude it. You can get the 3/4" thickness with the parallel offset tool before push-pull.

I just made the middle extrusion here, not the end caps. I noticed a bug I forgot about: preselecting lines before using parallel offset is a problem in the web version because you loose your selection when the fly-out menu happens. Infuriating. You can do it my first using the fly-out menu to get parallel offset on top, then switch to selection with the space bar, do the selection and go back to the parallel offset tool with one click.