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: For all z, if z takes a plane, then z is fast. For all z, if z takes a plane, then z is playing tennis. For all z, if z plays tennis, then z is taking a plane. There is at least one z for which if z were fast, then z is taking a plane.
For all z, if z plays tennis, then z is fast can be inferred via the universal transitivity rule. There is at least one z for which if z were fast, then z is playing tennis can be inferred via the existential transitivity rule. For all z, z will take a plane if and only if z will play tennis can be inferred via the universal biconditional introduction rule. For all z, z will play tennis if and only if z will take a plane can be inferred via the universal biconditional introduction rule. There is at least one z for which z is fast if and only if z will take a plane can be inferred via the existential biconditional introduction rule. There is at least one z for which z will take a plane if and only if z is fast can be inferred via the existential biconditional introduction rule.