Last section we learned how to extract P out of ~(P->Q). But remember, there’s another half to the problem.

~(P->Q) is equivalent to P&~Q.

~(P->Q) is equivalent to P&~Q. Now we have to figure out how to get ~Q.

Less setup is needed here, because you already know the general plan. We do a reductio, and we build P->Q from the inside in order to complete that reductio.

Here goes.

We use Reit to build P->Q.

Hopefully you can see why it’s called the reiteration trick. We use Reit to build P->Q.

Now that you can deal with ~(P->Q), you have all the proof skills you need to master PROP!

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