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Paul: Mark and I are still at Carkeek Park, upper level, in Seattle, Washington, in case we havent said so. Behind us is a little shelter and some woods. Then behind us is further back is Puget Sound. So were still at Carkeek Park. Theres a time for three more replacement rules, and that is these three will be the last of the replacement rules. First rule is very short and simple. Tautology says that you can take a formula P wedge P and replace it with the corresponding formula P, or vice versa. P can be replaced with P wedge P, anywhere in a proof. Similarly, the formula P ampersand P is interchangeable with the formula P, anywhere in a proof. So we can take an A and turn it into A wedge A. We can take an E and turn it into E ampersand E, and so forth. Next rule is, uhexportation. The exportation rule No, its okay. Well just keep going. Its a little minor slipup. Exportation rule says that if I have a statement P ampersand Q horseshoe R that thats interchangeable