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 x_1 is a carpenter if and only if x_1 will play tennis. For all x_1, if x_1 plays tennis, then x_1 is sad.
There is at least one x_1 for which if x_1 were a carpenter, then x_1 is playing tennis can be inferred via the existential biconditional elimination rule. There is at least one x_1 for which if x_1 plays tennis, then x_1 is a carpenter can be inferred via the existential biconditional elimination rule.