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- #1

Right off the bat, it looks like they've thrown me a curveball. The fact that [tex]v[/tex] does not occur free in [tex] \psi[/tex] means that the Existential Hypothesis rule is going to need some care when applied.

I've come up with two possible proofs:

..each in a different colour.

To me, the top proof looks more correct than the bottom. It's just the Existential Hypothesis rule that's throwing me.

For the first proof, I think line 10 is wrong. I need the existential hypothesis rule to depend on all the assumptions where v is free. This happens in lines 1,2 and MAYBE 3. If v is a free variable in line 3, then i'm sorted and everything is right. If it isn't, then I have a problem on my hands.

There's a similar problem for the second proof too.

Useful things:

The far left number show the assumptions a line depends on. The bracketed number is the line number and the far right column is the rules column.

As s = Assumption

UE = Universal Eradicator

Taut = Tautology

CP = Conditional Proposition

EH= Existential Hypothesis

Thanks in advance