If the logic involved come as a two-valued logic, then yes. However, if we have some other system of logic involved, perhaps, perhaps not. To see what's going on here, consider how from Np (the negation of p) we can legitimately infer Cpq (that's (p->q) in Polish notation). Now, "from Np, we may infer Cpq", though it could get used as such, doesn't usually get taken as a basic rule of inference for two-valued propositional logic. Instead, CNpCpq exists as a theorem of classical two-valued logic. Consequently if "Np" gets proven, then by application of modus ponendo ponens (the rule of detachment, conditional elimination), we can obtain "Cpq". So, we can simply obtain a proof for Cpq also by adding one "Cpq" to the end of the proof of "Np". So, basically if a system of logic has the rule of modus ponendo ponens, has CNpCpq as a logical theorem, then in order to prove Cpq, you just have to prove Np.