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Subformula replacement is the operation of replacing one specified subformula occurrence by another logical formula. Its preservation of well-formedness is the subformula replacement theorem.

Replacing one designated subformula occurrence in a propositional formula by another propositional formula preserves well-formedness. Induct on the context surrounding the occurrence: at the root the result is the replacement formula; under a connective apply the induction hypothesis to the affected child and rebuild the parent using its formation rule.