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 not bored. There is at least one y for which y will write a letter if and only if y is a nurse. For all y, y will write a letter if and only if y is bored.
For all y, if y writes a letter, then y is bored can be inferred via the universal biconditional elimination rule. There is at least one y for which if y writes a letter, then y is a nurse can be inferred via the existential biconditional elimination rule. For all y, if y were bored, then y is writing a letter can be inferred via the universal biconditional elimination rule. There is at least one y for which if y were a nurse, then y is writing a letter can be inferred via the existential biconditional elimination rule. For all y, y will not write a letter can be inferred via the universal biconditional elimination rule.