How to Rabbet into a Butted Corner?
New to the forum, fairly new to word working, but have general experience and fairly handy with an acceptable amount of tools. I'm working on building a workbench in which I want to recess the MDF sheet into the 2x4 frame. I plan on routing a rabbet into the inner edge of the 2x4 frame to make the space for the sheet to lay down flush. The issue I'm having is how to do this into the corner of the butted joint.
If I do a miter, I don't see the issue, just rabbet all the way through and the nice sharp corner for the MDF will be fine. But I don't like the miter for the strength (it's a rolling workbench) and sharpness (I want to have the corners rounded so they don't snag). So a butt joint is ideal, but I don't understand how to get a nice sharp corner with the router/rabbet approach. This image is an example how how I would like to end up, but I don't think they did a rabbet in this picture, just using as an example.
Look forwards to the responses, thanks for the help!