Suppose one wants to prove $P \implies Q$ by contradiction. In general, we will probably have the following, $P_1, \dots, P_n \implies Q$. Suppose we want to prove this by contradiction. Then is it better to get a contradiction via the following: $P_1, \dots, P_n, \neg Q\implies Q$? Or would is be better to get a contradiction via $P_1, \dots, P_n, \neg Q\implies \neg P_i$ for any $i \in \{1, \dots , n \}$? Is the second proof "stronger" than the first proof?
For the second proof, the assumption of $\neg Q$ could potentially come up with negations of all the $P_{i}$'s right?