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?

Classical and intuitionistic propositional logic do not prove the same formulas, even in the purely implicational fragment.
Most famously, Peirce's Law $((P\to Q)\to P)\to P$ is a classical tautology, but is not intuitionistically valid. (That is, classical logic proves it, but intuitionistic logic doesn't).

The two logics are equivalent for the $\{\land,\lor\}$ fragment, though. In terms of which formulas are theorem of the pure calculus, this is not very interesting (because no formula in the $\{\land,\lor\}$ fragment are theorems), but it also holds if you consider non-empty theories: Classical and intuitionistic entailment coincide for this fragment.
See this question which shows that the only change to the classical sequent calculus LK that is necessary to get intuitionistic logic instead is to the ${\to}R$ rule. However a cut-free proof in the sequent calculus never uses rules for connectives that don't appear in the conclusion, so the valid (cut-free) proofs in the classical LK for conclusions in the $\{\land,\lor\}$ fragment are the same as the valid proofs in the intuitionistic variant.
