Consider the following premises. There is at least one x_10 for which x_10 will make tea if and only if x_10 will play squash. For all x_10, if x_10 makes tea, then x_10 is a poet. For all x_10, x_10 will play squash. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 is not a poet.
 From the fact that there is at least one x_10 for which x_10 will make tea if and only if x_10 will play squash we can infer that there is at least one x_10 for which if x_10 plays squash, then x_10 is making tea via existential biconditional elimination. From the fact that there is at least one x_10 for which if x_10 plays squash, then x_10 is making tea, and that for all x_10, if x_10 makes tea, then x_10 is a poet we can infer that there is at least one x_10 for which if x_10 plays squash, then x_10 is a poet via existential transitivity. Finally, from the fact that there is at least one x_10 for which if x_10 plays squash, then x_10 is a poet, and that for all x_10, x_10 will play squash we can infer that there is at least one x_10 for which x_10 is a poet via existential modus ponens, which contradicts that For all x_10, x_10 is not a poet. Therefore, the answer is no.