Consider the following premises. If it is late, then Robert is climbing a mountain. For all x, if x climbs a mountain, then x is taking a plane. Robert is taking a plane. If Robert takes a plane, then it is late. Can we infer the following from them? If we can, name the inference rule being used: It is late.
 From the fact that for all x, if x climbs a mountain, then x is taking a plane we can infer that if Robert climbs a mountain, then Robert is taking a plane via universal instantiation. From the fact that if it is late, then Robert is climbing a mountain, and that if Robert climbs a mountain, then Robert is taking a plane we can infer that if it is late, then Robert is taking a plane via transitivity. From the fact that if Robert takes a plane, then it is late, and that if it is late, then Robert is taking a plane we can infer that Robert is taking a plane if and only if it is late via biconditional introduction. From the fact that Robert is taking a plane if and only if it is late we can infer that if Robert takes a plane, then it is late via biconditional elimination. Finally, from the fact that if Robert takes a plane, then it is late, and that Robert is taking a plane we can infer that it is late via modus ponens. Therefore, the answer is yes.