 For each formula \(A,\) \(g(A)\) is provable intuitionistically if and only if \(A\) is provable classically. In particular, if \(B \oldand \neg B\) were classically provable for some formula \(B,\) then \(g(B) \oldand \neg g(B)\) (which is \(g(B \oldand \neg B))\) would in turn be provable intuitionistically. Hence: