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, if y_1 works, then y_1 is writing a letter. There is at least one y_1 for which if y_1 writes a letter, then y_1 is working. For all y_1, y_1 will write a letter.
There is at least one y_1 for which y_1 will work can be inferred via the existential modus ponens rule. There is at least one y_1 for which y_1 will write a letter if and only if y_1 will work can be inferred via the existential biconditional introduction rule. There is at least one y_1 for which y_1 will work if and only if y_1 will write a letter can be inferred via the existential biconditional introduction rule.