https://maximummathematics.com/books/foundational-mathematics/proof/universal-generalization/index.htmlIn the previous section, we talked about a rule of inference that lets us go from broadly true statements to specifically true statements — if something is true for every member of a universe, we can pick out any element from that universe and be assured it still has whatever property we’re interested in. Up to now, none of the arguments we’ve examined have had a universally quantified statement as a conclusion — meaning none of our conclusions could have been generalized. Most results in mathematics are stated in general terms, not specific ones. The Pythagorean Theorem applies to every right triangle, not just isosceles ones, or ones with integer side lengths. The Quadratic Formula doesn’t apply only to $x^2 + 2x + 1 = 0$, or only to $x^2 - 6x + 9 = 0$ — it works even when the leading coefficient isn’t $1$, or when all the coefficients are irrational, or when the corresponding parabola doesn’t even intersect the $x$-axis.Hugoen-US