16 lines
1.1 KiB
Markdown
16 lines
1.1 KiB
Markdown
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| ---- | --------------------------- | ---------- | --------------------------------- |
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| 1 | $A \implies \lnot B$ | Premise | |
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| 2 | $(B \lor C) \lor D$ | Premise | |
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| 3 | $\lnot C \lor D \implies A$ | Premise | |
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| 4 | $\lnot C$ | Premise | |
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| 5 | $\lnot C \lor D$ | From 4 | $\lor Intro$ |
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| 6 | $A$ | From 3 & 5 | $\implies Elim$ Modus Ponens |
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| 7 | $\lnot B$ | From 1 & 6 | $\implies Elim$ Modus Ponens |
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| 8 | $\lnot B \land \lnot C$ | From 2 & 7 | $\land Intro$ |
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| 9 | $\lnot (B \lor C)$ | From 8 | De Morgans Law |
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| 10 | $D$ | From 9 | $\lor Elim$ Disjunctive Syllogism |
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B or C is not true, therefore D must be true from step 2. |