That was really interesting. Thanks for your time

Forgive me if I am incorrect, for I don't know too much about pure formal logic and it's symbols, but couldn't you prove --p = p in less lines?

This is what I'm thinking:

P = False (Premise)
-P = True = X (Definition of negation)
-X = False (Definition of negation)
Therefore, -X = --P = False = P (multiple definitions)

Is this incorrect?