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**Kiwili49** Hey everyone,

I am stuck on this proof and don't know what direction to take. I know what inconsistent means, but I don't know how to show $\displaystyle G_{\sigma} \vdash \lnot \sigma $.

Here is the problem...

Suppose that $\displaystyle G $ is an inconsistent set of sentences. For each $\displaystyle \sigma \in G $, let $\displaystyle G_{\sigma} $ be the set obtained by removing $\displaystyle \sigma $ from $\displaystyle G $. Prove

for any $\displaystyle \sigma \in G, G_{\sigma} \vdash \lnot \sigma $

Thanks!