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Full Idea
Universal quantification is prominent in logical practice but superfluous in theory, since (for all x)Fx obviously amounts to not(exists an x)not-Fx.
Gist of Idea
Universal quantification is widespread, but it is definable in terms of existential quantification
Source
Willard Quine (Philosophy of Logic [1970], Ch.2)
Book Ref
Quine,Willard: 'Philosophy of Logic' [Prentice-Hall 1970], p.25
A Reaction
The equivalence between these two works both ways, some you could take the universal quantifier as primitive instead, which would make general truths prior to particular ones. Is there something deep at stake here?