Hilbert systems are systems of deduction based on a large set of axioms and a minimal set of inference rules. Since deductions in Hilbert systems can be very hard to come up with, I will discuss some tips and tricks that I learned when I tried to solve this problem in Troelstra’s Basic Proof Theory:1 Prove that the following two sets of axioms are equivalent.2 System $A$: $P \imp (Q \imp P)$ $(P \imp Q \imp R) \imp (P \imp Q) \imp (P \imp R)$ System $B$:...