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Old 06-26-2008, 12:52 PM
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Re: Need help with simple proof

It's absolutely no problem at all. This is the only way you could successfully complete the proof with inference and replacement rules.

Basically, we derive (A&B)v(~A&~B) from A<-->B by means of the equivalence rule.

However, equivalence is a replacement rule. Still part of the basic rules, but more difficult to work with in bigger proofs.

Equivalence basically states that whenever P<-->Q is given, (P&Q)v(~P&~Q) or (P-->Q) & (Q-->P) can replace it... and vice versa because they basically mean the same thing.
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