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Given
1. P ≡ ~C
2. ~(P & D)
3. D
Prove C
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4. ~P v ~D 2 De Morgan's Law
5. ~D v ~P 4 Commutation
6. ~~D 3 Double Negation
7. ~P 5,6 Disjunctive Syllogism
8. (P -> ~C) * (~C -> P) 1 Material Equivalence
9. (~C -> P) * (P -> ~C) 8 Commutation
10. ~C -> P 9 Simplification
11. ~C -> ~~P 10 Double Negation
12. ~~C 11,7 Modus Tollens
13. C 12 Double Negation
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