With a truth table its easy to see that the two formulae $A\land B \to C$ and $A \to B \to C$ are not equivalent, for example, if $A = B = C = 0$, than the first evaluates to $1$ and the second to $0$ (because $A \to B$ is truth, and then $(A\to B) \to C$) is false).
it is referred to this transformation as currying, and there
on page 9 it is stated that
- Curry and Uncurry are proofs of $$\forall P,Q,R. (P \land Q) \to R \leftrightarrow (P \to Q \to R)$$
So i am confused, when are these expressions equivalent, and if not how can I use them for "uncurrying"?