Consider the following premises. q_1 <-> q_12. ~q_1. ~q_12 <-> w. Can we infer w from them? If possible, name the inference rules being used at each step.
 From q_1 <-> q_12, ~q_1 we can infer ~q_12 via biconditional elimination. From ~q_12 <-> w we can infer ~q_12 -> w via biconditional elimination. Finally, from ~q_12 -> w, ~q_12 we can infer w via modus ponens. Therefore, the answer is yes.