The hypothesis was that PA proves that “if PA proves C, then C” This enabled it to be proved that “PA proves C” So I think what we actually get applying the deduction theorem is ?((◻C)->C)->?C
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The hypothesis was that PA proves that “if PA proves C, then C” This enabled it to be proved that “PA proves C” So I think what we actually get applying the deduction theorem is ?((◻C)->C)->?C