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_8, x_8 will make tea if and only if x_8 is excited. For all x_8, if x_8 takes a plane, then x_8 is writing a letter. There is at least one x_8 for which if x_8 were excited, then x_8 is taking a plane.
There is at least one x_8 for which if x_8 were excited, then x_8 is writing a letter can be inferred via the existential transitivity rule. For all x_8, if x_8 makes tea, then x_8 is excited can be inferred via the universal biconditional elimination rule. For all x_8, if x_8 were excited, then x_8 is making tea can be inferred via the universal biconditional elimination rule.