Consider the following premises. q and q_10. q_1 -> w. q -> q_1. Can we infer w from them? If possible, name the inference rules being used at each step.
 From q and q_10 we can infer q via simplification. From q -> q_1, q_1 -> w we can infer q -> w via transitivity. Finally, from q -> w, q we can infer w via modus ponens. Therefore, the answer is yes.