I' installing new shower and trying to fit waste in cramped subfloor. This is the view from the basement with the p trap just loosely attached to the shower drain a bit behind the current waste pipes. The top of the main sewer waste stack is on the in the shadows on the right and has an open top to that wye. I'm wondering if I can just run the shower drain through the P-trap over to a straight dump down on the main sewer stack using a 3" to 2" reducer without creating an S trap. The main vent line is about 2 feet away to the left in this photo, and I would be dropping this on the top of the main sewer stack. Or, should I look at adding an air admittance valve if possible before the dump down? Thanks for your help.