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_2, y_2 will not write a letter. There is at least one y_2 for which y_2 will write a letter if and only if y_2 will go running. For all y_2, y_2 will go running if and only if y_2 will write a letter.
For all y_2, if y_2 goes running, then y_2 is writing a letter can be inferred via the universal biconditional elimination rule. There is at least one y_2 for which if y_2 writes a letter, then y_2 is running can be inferred via the existential biconditional elimination rule. For all y_2, if y_2 writes a letter, then y_2 is running can be inferred via the universal biconditional elimination rule. There is at least one y_2 for which if y_2 goes running, then y_2 is writing a letter can be inferred via the existential biconditional elimination rule. There is at least one y_2 for which y_2 will not go running can be inferred via the existential biconditional elimination rule. For all y_2, y_2 will not go running can be inferred via the universal biconditional elimination rule.