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: Joseph is reading a book if and only if Mary is sleeping. Mary is sleeping if and only if Jessica is working. Joseph is not poor. For all x_12, x_12 will read a book if and only if x_12 is poor.
If Joseph reads a book, then Mary is sleeping can be inferred via the biconditional elimination rule. If Mary sleeps, then Jessica is working can be inferred via the biconditional elimination rule. If Mary sleeps, then Joseph is reading a book can be inferred via the biconditional elimination rule. If Jessica works, then Mary is sleeping can be inferred via the biconditional elimination rule. For all x_12, if x_12 reads a book, then x_12 is poor can be inferred via the universal biconditional elimination rule. For all x_12, if x_12 were poor, then x_12 is reading a book can be inferred via the universal biconditional elimination rule.