Newton's "law" of gravitation is false. There is no conclusive proof of general relativity either.
I can't even begin to fathom how wrong that is.
Ok, pick something up. Anything. Now let go. See how it moves downward at an increasing speed? That's called gravity.
While you are right in the sense that newton's law of gravitation is more or less true, your proof falls short(though there is plenty of proof out there that doesn't). the best way I can explain this is with Einstein's thought experiment. lets say you are in a room with no windows and no doors. you stand on the floor without floating off. are you experiencing the effects of earth's gravity, or are you on a rocket that is accelerating. in this senario, you can't prove either.
this is why your proof is insufficient, and why the chair experiment is the same.
It is also a great metaphor for FEers living in a room with no windows refusing to look outside of it and see that there is proof of gravity outside that room.