This is the very beginning of my reformulations of mathematics. I am looking for others who want to explore this with me.
I mean there's probably some logician whose done something similar to this so I'd recommend looking over many foundations of mathematics to help you get a head start.
While the journey is long, if you want to create a new foundation to mathematics you'll need to see everything that has already been done. However there is no problem with you continuing with your ideas and maybe later on you learn about how similar or different it is to foundations of math.
Also I'm wondering if the 1 is all and all is one is a reference to full metal alchemist.