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 z for which if z were a writer, then z is playing squash. For all z, if z plays squash, then z is making tea. For all z, if z plays squash, then z is a writer. For all z, if z makes tea, then z is playing squash.
For all z, if z makes tea, then z is a writer can be inferred via the universal transitivity rule. There is at least one z for which if z were a writer, then z is making tea can be inferred via the existential transitivity rule. For all z, z will play squash if and only if z will make tea can be inferred via the universal biconditional introduction rule. For all z, z will make tea if and only if z will play squash can be inferred via the universal biconditional introduction rule. There is at least one z for which z is a writer if and only if z will play squash can be inferred via the existential biconditional introduction rule. There is at least one z for which z will play squash if and only if z is a writer can be inferred via the existential biconditional introduction rule.