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  "body": "\n## Statement\n\nWeakening statements by adding two negations before existential quantifiers (and atoms) is also the core step in the double-negation translation. It constitutes an embedding of classical first-order logic into intuitionistic logic: a first-order formula is provable in classical logic if and only if its Gödel–Gentzen translation is provable intuitionistically. For example, any theorem of classical propositional logic of the form $\\psi\\to\\phi$ has a proof consisting of an intuitionistic proof of $\\psi\\to\\neg\\neg\\phi$ followed by one application of double-negation elimination. Intuitionistic logic can thus be seen as a means of extending classical logic with constructive semantics.\n",
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