https://maximummathematics.com/books/foundational-mathematics/proof/proof-technique-contradiction/index.htmlAs discussed in the previous section, when trying to prove a statement like $p \to q$, we can take an indirect approach by proving some other statement, logically equivalent to $p \to q$, is true. There, the indirect method we used was the contrapositive. In this section, we use the Rule of Contradiction to arrive at another indirect proof method. The Underlying Argument Consider some arbitrary statement $p$. Since the implication $(\neg p \to F_0) \to p$ is always true (as we saw in the section on Rules of Inference), we can write $(\neg p \to F_0) \Longrightarrow p$ — meaning it’s a valid rule of inference, representing the valid argumentHugoen-US