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Jan 27, 2016 at 15:13 comment added Colin McLarty The technique is there, yes, but this result understates the result in OP's question, since co-validity is not the same thing as being a conservative extension. And on its face this theorem finds for each formula $\alpha$ two different formulas: one co-satisfiable with $\alpha$ and one co-valid, while OP cites a uniform translation from sentences using the function to sentences not, with an axiom making the two provably equivalent. Probably Bell and Machover somewhere state OP's result as OP states it but this theorem is not it.
Jan 27, 2016 at 13:47 vote accept Peter LeFanu Lumsdaine
Jan 27, 2016 at 13:12 history edited Håkon R. Gylterud CC BY-SA 3.0
Shortened google books link.
Jan 27, 2016 at 12:19 history answered Håkon R. Gylterud CC BY-SA 3.0