Consider the following premises. For all x_12, if x_12 climbs a mountain, then x_12 is happy. For all x_12, if x_12 were happy, then x_12 is climbing a mountain. Joseph is not climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: Joseph is happy.
 From the fact that for all x_12, if x_12 were happy, then x_12 is climbing a mountain, and that for all x_12, if x_12 climbs a mountain, then x_12 is happy we can infer that for all x_12, x_12 is happy if and only if x_12 will climb a mountain via universal biconditional introduction. From the fact that for all x_12, x_12 is happy if and only if x_12 will climb a mountain we can infer that Joseph is happy if and only if Joseph is climbing a mountain via universal instantiation. Finally, from the fact that Joseph is happy if and only if Joseph is climbing a mountain, and that Joseph is not climbing a mountain we can infer that Joseph is not happy via biconditional elimination, which contradicts that Joseph is happy. Therefore, the answer is no.