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Logica |
Tools
for
Thought
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1
p => ~p
Premise
2
p => (~p => ~(p => ~p))
Inconsistency Schema
3
(p => (~p => ~(p => ~p))) => ((p => ~p) => (p => ~(p => ~p)))
Implication Distribution Schema
4
(p => ~p) => (p => ~(p => ~p))
Implication Elimination
3
2
5
p => ~(p => ~p)
Implication Elimination
4
1
6
~~(p => ~p) => ~p
Contrapositive
5
7
(p => ~p) => ~~(p => ~p)
Negation Introduction Schema
8
(p => ~p) => ~p
Transitivity
6
7
9
~p
Implication Elimination
8
1
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