https://maximummathematics.com/books/foundational-mathematics/proof/logical-implications/index.htmlSo far, we’ve studied what an implication means on its own, and how it relates to variations like its converse, inverse, and contrapositive. Now we turn to a special kind of implication — one that’s true no matter what truth values its hypothesis and conclusion happen to take on. These implications are especially useful, since knowing one holds lets us deduce its conclusion with total certainty the moment its hypothesis is satisfied.Hugoen-US