https://maximummathematics.com/books/foundational-mathematics/proof/quantified-logical-implications/index.htmlNow that we’ve taken a closer look at the implication itself, let’s revisit quantified statements to see how the same ideas — logical implication, and the converse, inverse, and contrapositive — carry over to them. A Simple Logical Implication Suppose we have some open statement $p(x)$ with some non-empty universe $\mathcal{U}$ (non-empty just means $\mathcal{U}$ contains at least one element, which we can refer to as $\alpha$).Hugoen-US