My current progress 
here: 
https://github.com/metamath/set.mm/commit/4ea74c3d42b6f6fc8087b9fd2323285dedf76869

So far, I made almost all proofs by hand (in metamath.exe) without any 
help. The only exception is ~axk4, where after making a number of 
unsuccessful attempts I quickly peeked at Boolos book. I have the 
impression that there is basically only one idea that derives ~axk4 from 
~ax-gl, 
and if you don't find that idea then you're lost. Interestingly, the proof 
is pretty short once you get the right track. Some of the long ones were 
not easy too, but I got them in the end. I have not compared my proofs with 
the ones in the book (except for ~axk4), so maybe there are original ideas 
in here.

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