# Associativity of 'or' and 'and' in Hilbert Ackerman System

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?

• Maybe it is tume that you make explicit the reference to " Hilbert & Ackerman System"; the book has been published in 1928 and not many math log experts know it. – Mauro ALLEGRANZA Mar 5 '17 at 8:48
• See Th.16 and Th.17 of David Hilbert & Wilhelm Ackermann, Principles of Mathematical Logic (2nd ed, 1937), page 36. – Mauro ALLEGRANZA Mar 5 '17 at 8:51
• Thanks for the reference! Is there anywhere I can buy this as an ebook? On google its only available as a hardcover – Pablo Estrada Mar 5 '17 at 13:06