1. A -> D
2. ~C -> ~D
3. (C v D) -> ~C / therefore, A -> E
4. ~~D -> ~~C 2, contrapositive
5. D -> C 4, double negation
6. ~~C -> ~(C v D) 3, contrapositive
7. C -> ~(C v D) 6, double negation
8. C -> (~C & ~D) 7, DeMorgan's law
9. (C -> ~C) & (C -> ~D) 8, composition
10. C -> ~C 9, simplification
11. ~C v ~C 10, material implication
12. ~C 11, simplification
13. ~C v E 12, addition
14. A -> C 1,5, hypothetical syllogism
15. C -> E 13, material implication
16. A -> E 14,15, hypothetical syllogism
Edwin
