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Full Idea
The elimination rule for the universal quantifier concerns the use of a universal proposition as a premiss to establish some conclusion, whilst the introduction rule concerns what is required by way of a premiss for a universal proposition as conclusion.
Gist of Idea
Universal elimination if you start with the universal, introduction if you want to end with it
Source
E.J. Lemmon (Beginning Logic [1965], 3.2)
Book Ref
Lemmon,E.J.: 'Beginning Logic' [Nelson 1979], p.104
A Reaction
So if you start with the universal, you need to eliminate it, and if you start without it you need to introduce it.
13907 | If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon] |
13901 | Predicate logic uses propositional connectives and variables, plus new introduction and elimination rules [Lemmon] |
13903 | Universal elimination if you start with the universal, introduction if you want to end with it [Lemmon] |
13904 | Universal Elimination (UE) lets us infer that an object has F, from all things having F [Lemmon] |
13906 | With finite named objects, we can generalise with &-Intro, but otherwise we need ∀-Intro [Lemmon] |
13908 | UE all-to-one; UI one-to-all; EI arbitrary-to-one; EE proof-to-one [Lemmon] |