Consider the following premises. If Joseph plays squash, then Mary is playing tennis. It is sunny or Joseph is playing squash. If it is sunny, then Mary is playing tennis. If Mary plays tennis, then it is sunny. Can we infer the following from them? If we can, name the inference rule being used: Mary is playing tennis.
 From the fact that if it is sunny, then Mary is playing tennis, and that if Mary plays tennis, then it is sunny we can infer that it is sunny if and only if Mary is playing tennis via biconditional introduction. From the fact that it is sunny if and only if Mary is playing tennis we can infer that if it is sunny, then Mary is playing tennis via biconditional elimination. Finally, from the fact that if it is sunny, then Mary is playing tennis, that if Joseph plays squash, then Mary is playing tennis, and that it is sunny or Joseph is playing squash we can infer that Mary is playing tennis via disjunction elimination. Therefore, the answer is yes.