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Gödel’s second incompleteness theorem does not apply to Hilbert’s approach to proving consistency in the way it was previously thought. This is because Hilbert’s understanding of consistency as a series of claims “D is consistent” for each PA-derivation D is not provably in PA equivalent to the Gödelian consistency formula Con(PA). Kripke showed in 2022 that Hilbert’s epsilon-substitution method for PA, HES, fails for non-Gödelian reasons. We modify HES to prove the Hilbertian consistency of PA within PA. As expected, our proof of consistency does not yield a PA-derivation of Con(PA). This undermines the unprovability of consistency thesis that “there exists no consistency proof of a system that can be formalized in the system itself” (Encyclopedia Britannica).