Consider the following premises. For all x, if x plays squash, then x is cooking. If David writes a letter, then Barbara is playing squash. David is writing a letter. Can we infer the following from them? Barbara is cooking.
 From the fact that for all x, if x plays squash, then x is cooking we can infer that if Barbara plays squash, then Barbara is cooking. From the fact that if David writes a letter, then Barbara is playing squash, and that David is writing a letter we can infer that Barbara is playing squash. Finally, from the fact that if Barbara plays squash, then Barbara is cooking, and that Barbara is playing squash we can infer that Barbara is cooking. Therefore, the answer is yes.