https://maximummathematics.com/books/foundational-mathematics/proof/proof-technique-direct-proofs/index.htmlAt this point, we’ve talked a lot about mathematical logic, arguments, and some common terminology. In this section, we introduce a method for providing a proof for a proposition — the most straightforward technique we have at our disposal. The Underlying Argument Consider a statement such as $p \to q$ — but remember that a theorem is almost always implicitly universally quantified, so what we really want to show is $\forall x\ [p(x) \to q(x)]$ for every element $x$ within some universe $\mathcal{U}$. How would we show this is always true?Hugoen-US