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