Consider the following premises. For all y, if y were a mechanic, then y is running. For all y, if y goes running, then y is reading a book. For all y, if y were a mechanic, then y is running. For all y, if y reads a book, then y is a mechanic. Can we infer the following from them? If we can, name the inference rule being used: For all y, if y goes running, then y is a mechanic.
We can infer this via the universal transitivity rule. Therefore, the answer is yes.