Consider the following premises. Thomas is an electrician or it is overcast. Elisabeth is climbing a mountain if and only if Thomas is an electrician. If it is overcast, then Elisabeth is climbing a mountain. Can we infer the following from them? Elisabeth is climbing a mountain.
 From the fact that Elisabeth is climbing a mountain if and only if Thomas is an electrician we can infer that if Thomas were an electrician, then Elisabeth is climbing a mountain. Finally, from the fact that if Thomas were an electrician, then Elisabeth is climbing a mountain, that if it is overcast, then Elisabeth is climbing a mountain, and that Thomas is an electrician or it is overcast we can infer that Elisabeth is climbing a mountain. Therefore, the answer is yes.