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    For every formula A, g(A) is provable intuitionistically ... — Carmelics
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    Supports→If classical logic were inconsistent, intuitionistic logic would also be inconsistent

    For every formula A, g(A) is provable intuitionistically if and only if A is provable classically

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    If B ∧ ¬B were classically provable for some formula B, then g(B) ∧ ¬g(B) would ...If classical logic were inconsistent, intuitionistic logic would also be inconsi...

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    If B ∧ ¬B were classically provable for some formula B, then g(B) ∧ ¬g...

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    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:

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