Consider the following premises. For all x_1, if x_1 cooks, then x_1 is rich. For all x_1, if x_1 were rich, then x_1 is a taxi driver. There is at least one x_1 for which if x_1 were curious, then x_1 is cooking. For all x_1, if x_1 were a taxi driver, then x_1 is curious. Can we infer the following from them? There is at least one x_1 for which x_1 is a taxi driver if and only if x_1 is curious.
 From the fact that for all x_1, if x_1 cooks, then x_1 is rich, and that for all x_1, if x_1 were rich, then x_1 is a taxi driver we can infer that for all x_1, if x_1 cooks, then x_1 is a taxi driver. From the fact that there is at least one x_1 for which if x_1 were curious, then x_1 is cooking, and that for all x_1, if x_1 cooks, then x_1 is a taxi driver we can infer that there is at least one x_1 for which if x_1 were curious, then x_1 is a taxi driver. Finally, from the fact that for all x_1, if x_1 were a taxi driver, then x_1 is curious, and that there is at least one x_1 for which if x_1 were curious, then x_1 is a taxi driver we can infer that there is at least one x_1 for which x_1 is a taxi driver if and only if x_1 is curious. Therefore, the answer is yes.