5) The proof in the Hilbert deductive system of a theorem known as conjunction elimination is provided. Write to the right of each step the number of the axiom or the name of the inference rule used. Note that the justification of the last step is already given.

	Theorem conjunction elimination Let A and B be arbitrary formulas of propositional logic. Then A B A

Proof

1.	A (B A)
2.	(B A) A
3.	(B A) A
4.	A B A	3, definition of operator ((B A) A B)

6) Prove in the Hilbert deductive system the expression given in Problem 3.8 of the textbook:

{A} (B A) B

The first two steps of the proof, as well as the inference rule to be used in the third step, are given. You are required to complete the third step and give the subsequent steps of the proof.

1.	{A, B A} A	Assumption
2.	{A, B A} B A	Assumption
3.		2, contrapositive rule (2)