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: If Barbara sleeps, then Richard is happy. Richard is writing a letter. For all x_10, x_10 is happy if and only if x_10 will write a letter.
There is at least one x for which x will write a letter can be inferred via the existential generalization rule. For all x_10, if x_10 were happy, then x_10 is writing a letter can be inferred via the universal biconditional elimination rule. For all x_10, if x_10 writes a letter, then x_10 is happy can be inferred via the universal biconditional elimination rule.