Consider the following premises. Karen is not climbing a mountain. If it snows, then Linda is an office clerk. Karen is climbing a mountain if and only if David is an astronaut. If Linda were an office clerk, then it is snowing. David is an astronaut if and only if Linda is an office clerk. Can we infer the following from them? Patricia is not writing a letter.
We cannot infer that from the premises. Therefore the answer is no.