Consider the following premises. For all x, x is a bartender or x will not read a book. For all x, x is a bartender if and only if x is a cashier. Can we infer the following from them? For all x, if x reads a book, then x is a cashier.
 From the fact that for all x, x is a bartender or x will not read a book we can infer that for all x, if x reads a book, then x is a bartender. From the fact that for all x, x is a bartender if and only if x is a cashier we can infer that for all x, if x were a bartender, then x is a cashier. Finally, from the fact that for all x, if x reads a book, then x is a bartender, and that for all x, if x were a bartender, then x is a cashier we can infer that for all x, if x reads a book, then x is a cashier. Therefore, the answer is yes.