SOLUTION: Could you please help me construct a proof for this problem? 1. (G -> H) -> J conclusion is H -> J

Question 297356: Could you please help me construct a proof for this problem?
1. (G -> H) -> J conclusion is H -> J

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

1.  (G -> H) -> J           :.  H -> J
--------------------------------------
2.  (~G v H) -> J                     1    Material Implication
3.  ~(~G v H) v J                     2    Material Implication
4.  (~~G * ~H) v J                    3    De Morgan's Law
5.  (G * ~H) v J                      4    Double Negation
6.  J v (G * ~H)                      5    Commutation
7.  (J v G) * (J v ~H)                6    Distribution
8.  (J v ~H) * (J v G)                7    Commutation
9.  J v ~H                            8    Simplification
10. ~H v J                            9    Commutation
11.  H -> J                           10   Material Implication

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