Full Idea
None of the classical ways of defining one logical constant in terms of others is available in intuitionist logic (and this includes the two quantifiers).
Gist of Idea
Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism
Source
David Bostock (Philosophy of Mathematics [2009], 7.2)
Book Reference
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.214