Full Idea
If there are just three objects and each has F, then by an extension of &I we are sure everything has F. This is of no avail, however, if our universe is infinitely large or if not all objects have names. We need a new device, Universal Introduction, UI.
Clarification
A 'universe' is usually now called a 'domain'
Gist of Idea
With finite named objects, we can generalise with &-Intro, but otherwise we need ∀-Intro
Source
E.J. Lemmon (Beginning Logic [1965], 3.2)
Book Reference
Lemmon,E.J.: 'Beginning Logic' [Nelson 1979], p.106