https://maximummathematics.com/books/foundational-mathematics/proof/a-closer-look-at-the-implication/index.htmlOut of the two conditional-style connectives we’ve seen — the implication $p \to q$ and the biconditional $p \leftrightarrow q$ — we’ve given the biconditional a fairly thorough treatment already. Now we turn back to the implication, to see what else it has to offer. Recall from its definition that the implication $p \to q$ is false exactly when $p$ is true and $q$ is false. In other words, $\text{true} \to \text{false}$ is a false proposition. This deserves special emphasis:Hugoen-US