SOLUTION: Use Conditional Proof to solve the following argument E ⊃ (F ⊃ G) H ⊃ (G ⊃ I) (F ⊃ I) ⊃ (J v ~H) / (E•H) ⊃ J

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Question 1157960: Use Conditional Proof to solve the following argument
E ⊃ (F ⊃ G)
H ⊃ (G ⊃ I)
(F ⊃ I) ⊃ (J v ~H) / (E•H) ⊃ J
Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!
Use Conditional Proof to solve the following argument 
 1.  E ⊃ (F ⊃ G)
 2.  H ⊃ (G ⊃ I)
 3.  (F ⊃ I) ⊃ (J v ~H)                 / (E • H) ⊃ J

                            | 4.  E • H        Assumption for Conditional Proof   
                            | 5.  E            4, Simplification
                            | 6.  F ⊃ G        1,5, Modus Ponens
                            | 7.  H • E        4, Commutation
                            | 8.  H            6, Simplification
                            | 9.  G ⊃ I        2,8, Modus Ponens
                            |10.  F ⊃ I        6,9, Hypothetical Syllogism 
                            |11.  J v ~H       3,10, Modus Ponens
                            |12.  ~H v J       11, Commutation
                            |13.  ~~H          8, Double negation
                            |14.  J            12, Disjunctive Syllogism
15. (E • H) ⊃ J         Lines 4-14      Conditional Proof

Edwin
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