I wonder how to give a formal, Fitch-style, proof of P v $\displaystyle \neg$ P ..?

I am able to prove it by contradiction when I use that $\displaystyle \neg$ P & P is a tautological consequence of $\displaystyle \neg$ (P v $\displaystyle \neg$ P ) . But in order to prove this (one of the DeMorgan's laws I think?) formally I have to use the law of excluded middle itself...

I also know how to show these tautologies with truth tables, but an exercise explicitly ask for a formal proof of P v $\displaystyle \neg$ P .

All help is appreciated