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_1, y_1 will work if and only if y_1 will play squash. For all y_1, if y_1 plays squash, then y_1 is poor. For all y_1, y_1 will not work. There is at least one y_1 for which if y_1 were poor, then y_1 is playing squash.
There is at least one y_1 for which y_1 is poor if and only if y_1 will play squash can be inferred via the existential biconditional introduction rule. There is at least one y_1 for which y_1 will play squash if and only if y_1 is poor can be inferred via the existential biconditional introduction rule. For all y_1, if y_1 works, then y_1 is playing squash can be inferred via the universal biconditional elimination rule. For all y_1, if y_1 plays squash, then y_1 is working can be inferred via the universal biconditional elimination rule. For all y_1, y_1 will not play squash can be inferred via the universal biconditional elimination rule.