Question 388751
<pre>
1.  ~B v [ (C -> D) * (E -> D)]
2.  B * (C v E)                  /:. D
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3.  (C v E) * B                 2      Commutation
4.  B                           2      Simplification
5.  C v E                       3      Simplification
6.  E v C                       5      Commutation
7.  ~~E v C                     6      Double Negation
8.  ~E -> C                     7      Material Implication
9.  (C -> D) * (E -> D)         1,4    Modus Ponens
10. (E -> D) * (C -> D)         9      Commutation
11. C -> D                      9      Simplification
12. E -> D                      10     Simplification
13. ~D -> ~E                    12     Transposition
14. ~E -> D                     8,11   Hypothetical Syllogism
15. ~D -> D                     13,14  Hypothetical Syllogism
16. ~~D v D                     15     Material Implication   
17. D v D                       16     Double Negation
18. D                           17     Tautology
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