

Logica 
Tools for Thought


1
~~p => (~~~~p => ~~p)
Implication Creation Schema
2
(~~~~p => ~~p) => (~p => ~~~p)
Implication Reversal Schema
3
~~p => (~p => ~~~p)
Transitivity
1
2
4
(~p => ~~~p) => (~~p => p)
Implication Reversal Schema
5
~~p => (~~p => p)
Transitivity
3
4
6
(~~p => (~~p => p)) => ((~~p => ~~p) => (~~p => p))
Implication Distribution Schema
7
(~~p => ~~p) => (~~p => p)
Implication Elimination
6
5
8
~~p => ~~p
Identity Schema
9
~~p => p
Implication Elimination
7
8
