Consider the following premises. For all x_10, x_10 will not play squash. For all x_10, x_10 will work if and only if x_10 is happy. For all x_10, x_10 will play squash or x_10 is a poet. For all x_10, if x_10 were a poet, then x_10 is working. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 is happy.
 From the fact that for all x_10, x_10 will play squash or x_10 is a poet, and that for all x_10, x_10 will not play squash we can infer that for all x_10, x_10 is a poet via universal disjunctive syllogism. From the fact that for all x_10, if x_10 were a poet, then x_10 is working, and that for all x_10, x_10 is a poet we can infer that for all x_10, x_10 will work via universal modus ponens. From the fact that for all x_10, x_10 will work if and only if x_10 is happy we can infer that for all x_10, if x_10 works, then x_10 is happy via universal biconditional elimination. Finally, from the fact that for all x_10, if x_10 works, then x_10 is happy, and that for all x_10, x_10 will work we can infer that for all x_10, x_10 is happy via universal modus ponens. Therefore, the answer is yes.