I´m trying to prove a theorem on the Hilbert System where I find useful for the proof to use the theorems:
$\vdash x\lor (y\lor z) \rightarrow (x\lor y) \lor z$
$\vdash x\land (y\land z) \rightarrow (x\land y) \land z$
I know that is true because obviously the and and or operators are associtative. However I'm having a though time trying to prove the theorem using the Hilbert-Ackerman axioms and deduction rules. Can anyone guide me in the construction of the proofs?