Consider the following premises. w -> q_1. p_8 <-> w. q_1 -> p_8. Can we infer w <-> p_8 from them? If possible, name the inference rules being used at each step.
 From p_8 <-> w we can infer p_8 -> w via biconditional elimination. From w -> q_1, q_1 -> p_8 we can infer w -> p_8 via transitivity. Finally, from w -> p_8, p_8 -> w we can infer w <-> p_8 via biconditional introduction. Therefore, the answer is yes.