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: There is at least one x_1 for which if x_1 works, then x_1 is a bartender. For all x_1, if x_1 were a bartender, then x_1 is writing a letter. For all x_1, x_1 will work.
There is at least one x_1 for which x_1 is a bartender can be inferred via the existential modus ponens rule. There is at least one x_1 for which if x_1 works, then x_1 is writing a letter can be inferred via the existential transitivity rule.