Consider the following premises. For all x_10, if x_10 were a poet, then x_10 is fast. For all x_10, if x_10 were fast, then x_10 is taking a plane. For all x_10, if x_10 takes a plane, then x_10 is fast. There is at least one x_10 for which x_10 is a poet or x_10 will take a plane. For all x_10, if x_10 were fast, then x_10 is a poet. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 is fast.
 From the fact that for all x_10, if x_10 were a poet, then x_10 is fast, and that for all x_10, if x_10 were fast, then x_10 is a poet we can infer that for all x_10, x_10 is a poet if and only if x_10 is fast via universal biconditional introduction. From the fact that for all x_10, if x_10 were fast, then x_10 is taking a plane, and that for all x_10, if x_10 takes a plane, then x_10 is fast we can infer that for all x_10, x_10 is fast if and only if x_10 will take a plane via universal biconditional introduction. From the fact that for all x_10, x_10 is a poet if and only if x_10 is fast we can infer that for all x_10, if x_10 were a poet, then x_10 is fast via universal biconditional elimination. From the fact that for all x_10, x_10 is fast if and only if x_10 will take a plane we can infer that for all x_10, if x_10 takes a plane, then x_10 is fast via universal biconditional elimination. Finally, from the fact that for all x_10, if x_10 were a poet, then x_10 is fast, that for all x_10, if x_10 takes a plane, then x_10 is fast, and that there is at least one x_10 for which x_10 is a poet or x_10 will take a plane we can infer that there is at least one x_10 for which x_10 is fast via existential disjunction elimination. Therefore, the answer is yes.