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 y, y is a writer if and only if y will play squash. For all y, y will go running if and only if y is a carpenter. For all y, y is not a writer. For all y, y will play squash if and only if y is a carpenter.
For all y, if y were a writer, then y is playing squash can be inferred via the universal biconditional elimination rule. For all y, if y goes running, then y is a carpenter can be inferred via the universal biconditional elimination rule. For all y, if y plays squash, then y is a carpenter can be inferred via the universal biconditional elimination rule. For all y, if y plays squash, then y is a writer can be inferred via the universal biconditional elimination rule. For all y, if y were a carpenter, then y is running can be inferred via the universal biconditional elimination rule. For all y, if y were a carpenter, then y is playing squash can be inferred via the universal biconditional elimination rule. For all y, y will not play squash can be inferred via the universal biconditional elimination rule.