I've been reading the Stanford Encyclopedia of Philosophy article on classical logic, and I've been confused about Theorem 9, and the preceding statement. They mention how (*), the clause which states that any conclusion deducible from a set of premises is deduced by some nonempty set of the rules above, and state how this allows us to deduce that the number of steps is finite.
However, I'm confused as to how we derived such a conclusion from our deductive system. What problem does it pose for the deductive system the article posits if we have a deduction with infinite steps? I am intuitively skeptical of such a deduction, but I don't see a logical problem with the assertion. None, at least, which are derived from clause (*)
What am I missing?
Edit 1: While I am thankful for the responses from @Conifold and @Mauro ALLEGRANZA, I fear I have not been clear enough in what my confusion is. It makes sense that a valid derivation must be of finite length. My confusion is with the article linked, and how they derive this conclusion.
Edit 2: On request, the specific statement I'm having trouble with is the following: "By clause (*), all derivations are established in a finite number of steps". For reference, the clause posits that all derivations are performed by a combination of the introduction and elimination rules and the rule that you can deduce sentence s from any set of sentences L such that "s is an element of L."