SOLUTION: Use natural deduction to prove the following logical truth: // [F • (D ⊃ ∼ F)] ⊃ (D ⊃ A)

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Question 1188428: Use natural deduction to prove the following logical truth:
// [F • (D ⊃ ∼ F)] ⊃ (D ⊃ A)
Answer by RBryant(14)   (Show Source): You can put this solution on YOUR website!
Q:
// [F • (D ⊃ ∼ F)] ⊃ (D ⊃ A)    

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1.     [F • (D ⊃ ∼ F)] ⊃ (D ⊃ A)             Assumption
2.         [F • (D ⊃ ∼ F)]                    Assumption
3.              D                              Assumption
4.              F                              2              & Intro 
5.              D ⊃ ~F                         2              & Intro
6.              ~F                             3,5            ⊃ Elim 
7.              F • ~F                         4,6            & Intro
8.           A                                 7              Falsum Intro
9.      D ⊃ A                                 3-8             ⊃ Intro
10.  [F • (D ⊃ ∼ F)] ⊃ (D ⊃ A)               2-9             ⊃ Intro
                                                                        QED


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