Equivalence between fragments of intuitionistic and classical logics Is the fragment $\{\vee,\land,\Rightarrow\}$ (no $\neg$) of intuitionistic propositional logic equivalent to the corresponding fragment of classical propositional logic, i.e. a formula is intuitionistic provable iff it is classically valid?  If yes, where can I find such a proof?

Additionally to Henning's answer:
Usually you have at least some expression in your logic expressing "contradiction", for example $0=1$ in Heyting Arithmetic. Then you immediately get all of intuitionistic logic by setting $\neg a :\equiv a \Rightarrow (0 = 1)$, so removing $\neg$ usually does not change anything. 
If you don't have contradiction already, you can just "adjoin" it in the same fashion you add an $-\infty$ to the lattice of reals (and more generally: a least element to a poset or initial object to a category).
