1. 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)