Consider the following premises. For all x_6, if x_6 were happy, then x_6 is a mechanic. For all x_6, x_6 is happy or x_6 is a janitor. There is at least one x_6 for which if x_6 were a mechanic, then x_6 is curious. For all x_6, x_6 is curious or x_6 is not a janitor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 is curious.
 From the fact that for all x_6, if x_6 were happy, then x_6 is a mechanic, and that there is at least one x_6 for which if x_6 were a mechanic, then x_6 is curious we can infer that there is at least one x_6 for which if x_6 were happy, then x_6 is curious via existential transitivity. From the fact that for all x_6, x_6 is curious or x_6 is not a janitor we can infer that for all x_6, if x_6 were a janitor, then x_6 is curious via universal rewriting. Finally, from the fact that there is at least one x_6 for which if x_6 were happy, then x_6 is curious, that for all x_6, if x_6 were a janitor, then x_6 is curious, and that for all x_6, x_6 is happy or x_6 is a janitor we can infer that there is at least one x_6 for which x_6 is curious via existential disjunction elimination. Therefore, the answer is yes.