What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: There is at least one x for which if x plays tennis, then x is a poet. For all x, if x takes a plane, then x is playing tennis. For all x, if x plays tennis, then x is taking a plane. For all x, if x were a poet, then x is playing tennis.
For all x, if x were a poet, then x is taking a plane can be inferred via the universal transitivity rule. There is at least one x for which if x takes a plane, then x is a poet can be inferred via the existential transitivity rule. For all x, x will take a plane if and only if x will play tennis can be inferred via the universal biconditional introduction rule. For all x, x will play tennis if and only if x will take a plane can be inferred via the universal biconditional introduction rule. There is at least one x for which x will play tennis if and only if x is a poet can be inferred via the existential biconditional introduction rule. There is at least one x for which x is a poet if and only if x will play tennis can be inferred via the existential biconditional introduction rule.