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Title does not display the proof because the formula would break the character limit.

Presently working on proving the following identity:

$(\lnot P \lor Q)\land(\lnot Q \lor R) \equiv (\lnot P \lor R) \land[(P \leftrightarrow Q) \lor (R \leftrightarrow Q)]$

I tried applying the distributivity of the disjunction over the two biconditional statements on the RHS hoping it would lead somewhere, but after a lot of writing it seemed I'd only needlessly complicated the problem. I'm working off the assumption that most of the work needs to be done to the RHS.

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The following proof uses the law of the excluded middle to reach the goal:

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The overall strategy of the first part was to use the law of the excluded middle on $Q \lor \lnot Q$ to derive the right hand side of the equivalence from the left hand side.

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Again for the second part the law of the excluded middle on $Q \lor \lnot Q$ was used as the main strategy to derive the left hand side from the right hand side.

The proof concludes with the biconditional introduction.

Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/

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