Lรถb proved the following: for any C, Provable(Provable(C)->C)->Provable(C).
So, we may derive from PA soundness, that for any C, Provable(Provable(C)->C)->C.
Nobody proved, as you stated, that for any C (Provable(C)->C)->C.
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Lรถb proved the following: for any C, Provable(Provable(C)->C)->Provable(C).
So, we may derive from PA soundness, that for any C, Provable(Provable(C)->C)->C.
Nobody proved, as you stated, that for any C (Provable(C)->C)->C.