Consider the following premises. For all x_7, if x_7 were a musician, then x_7 is writing a letter. There is at least one x_7 for which x_7 will climb a mountain or x_7 is a poet. For all x_7, x_7 will not climb a mountain or x_7 is a musician. For all x_7, x_7 will write a letter if and only if x_7 is a poet. Can we infer the following from them? There is at least one x_7 for which x_7 will write a letter.
 From the fact that for all x_7, x_7 will write a letter if and only if x_7 is a poet we can infer that for all x_7, if x_7 were a poet, then x_7 is writing a letter. From the fact that there is at least one x_7 for which x_7 will climb a mountain or x_7 is a poet, and that for all x_7, x_7 will not climb a mountain or x_7 is a musician we can infer that there is at least one x_7 for which x_7 is a poet or x_7 is a musician. Finally, from the fact that for all x_7, if x_7 were a poet, then x_7 is writing a letter, that for all x_7, if x_7 were a musician, then x_7 is writing a letter, and that there is at least one x_7 for which x_7 is a poet or x_7 is a musician we can infer that there is at least one x_7 for which x_7 will write a letter. Therefore, the answer is yes.