You lost me at your "inverse law" step. Does that big "T" mean p and not p is true for all values of p?
It would be a contradiction if this were an actual proof and you implied something (namely that it is not the case that if p then r implies p). All I see is that this is false for all values of p, q, and r, since p and not p can never be true.
At least you recognize contradiction here, and you deduced (or I assume you did) that if p then r implies p.