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7/25/2019 Proof Tautology
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[(p q) (q r)] (p r) (Definition)
[(p q) (q p) (q r) (r q)] [(p r) (r p)] ( )
[(p q) (q p) (q r) (r q)] [(p r) (r p] (De Morgan)
[(p q) q] [(p q) p]
[(q r) r] [(q r) q]
[(p r) (r p)] (Distributivity)
[(p q) (q q)] [(p p) (q p)]
[(q r) (r r)] [(q q) (r q)]
[(p r) (r p] (Distributivity)
[(p q) T] [T (q p)]
[(q r) T] [T (r q)]
[(p r) (r p)] (Negation)
[(p q) (q p)] [(q r) (r q)] [(p r) (r p)] (Identity)
[(p q) (q p)] (q r)
[(p q) (q p)] (r q)
[(p r) (r p)] (Distributivity)
[(p q) (q r)] [(q p) (q r)]
[(p q) (r q)] [(q p) (r q)]
[(p r) (r p)] (Distributivity)
[(p q) (q r)] [(q q) (p r)]
[(q q) (p r)] [(q p) (r q)]
[(p r) (r p)] (Associativity)
[(p q) (q r)] [T (p r)]
[T (p r)] [(q p) (r q)]
[(p r) (r p)] (Negation)
[(p q) (q r)] T
T [(q p) (r q)]
[(p r) (r p)] (Domination)
[(p q) (q r)] [(q p) (r q)]
[(p r) (r p)] (Identity)
[(p q) (q r)] [(p r) (r p)]
[(q p) (r q)] [(p r) (r p)]
(Distributivity)
[(p q) (q r)] (p r)
[(p q) (q r)] (r p)
[(q p) (r q)] (p r)
[(q p) (r q)] (r p)
(Distributivity)
[(p p) q q r r] [(r r) p q q p]
[(r r) q p q p] [(p p) q r q r]
(Associativity)
[T q q r r] [T p q q p]
[T q p q p] [T q r q r]
(Negation)
(T T) (T T) (Domination)
T T T T (Associativity)
T (Identity)