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 x_6, if x_6 writes a letter, then x_6 is sleeping. There is at least one x_6 for which if x_6 sleeps, then x_6 is writing a letter. For all x_6, x_6 will sleep.
There is at least one x_6 for which x_6 will write a letter can be inferred via the existential modus ponens rule. There is at least one x_6 for which x_6 will sleep if and only if x_6 will write a letter can be inferred via the existential biconditional introduction rule. There is at least one x_6 for which x_6 will write a letter if and only if x_6 will sleep can be inferred via the existential biconditional introduction rule.