Consider the following premises. For all x, x will write a letter or x will climb a mountain. For all x, if x climbs a mountain, then x is taking a plane. For all x, if x writes a letter, then x is taking a plane. There is at least one x for which x will take a plane if and only if x 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 for which x is a poet.
 From the fact that for all x, if x writes a letter, then x is taking a plane, that for all x, if x climbs a mountain, then x is taking a plane, and that for all x, x will write a letter or x will climb a mountain we can infer that for all x, x will take a plane via universal disjunction elimination. From the fact that there is at least one x for which x will take a plane if and only if x is a poet we can infer that there is at least one x for which if x takes a plane, then x is a poet via existential biconditional elimination. Finally, from the fact that there is at least one x for which if x takes a plane, then x is a poet, and that for all x, x will take a plane we can infer that there is at least one x for which x is a poet via existential modus ponens. Therefore, the answer is yes.