Consider the following premises. For all x_4, if x_4 were excited, then x_4 is a cashier. For all x_4, x_4 is a cashier if and only if x_4 will climb a mountain. Can we infer the following from them? For all x_4, if x_4 were excited, then x_4 is climbing a mountain.
 From the fact that for all x_4, x_4 is a cashier if and only if x_4 will climb a mountain we can infer that for all x_4, if x_4 were a cashier, then x_4 is climbing a mountain. Finally, from the fact that for all x_4, if x_4 were excited, then x_4 is a cashier, and that for all x_4, if x_4 were a cashier, then x_4 is climbing a mountain we can infer that for all x_4, if x_4 were excited, then x_4 is climbing a mountain. Therefore, the answer is yes.