I'll rephrase it this way:
For all C:
Either provable(C) or not(provable(C))
If provable(C), then provable(C)
If not provable(C), then use the above logic to prove provable C.
Therefore all C are provable.
Which "above logic" are you referring to? If you mean your OP, I don't think that the logic holds, for reasons that I've explained in my replies.
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