| |
|
Logica |
Tools
for
Thought
|
|
1
p => (q => r)
Premise
2
(p => (q => r)) => (q => (p => (q => r)))
Implication Creation Schema
3
q => (p => (q => r))
Implication Elimination
2
1
4
(p => (q => r)) => ((p => q) => (p => r))
Implication Distribution Schema
5
((p => (q => r)) => ((p => q) => (p => r))) => (q => ((p => (q => r)) => ((p => q) => (p => r))))
Implication Creation Schema
6
q => ((p => (q => r)) => ((p => q) => (p => r)))
Implication Elimination
5
4
7
q => ((p => q) => (p => r))
Conditional Deduction
3
6
8
(q => ((p => q) => (p => r))) => ((q => (p => q)) => (q => (p => r)))
Implication Distribution Schema
9
(q => (p => q)) => (q => (p => r))
Implication Elimination
8
7
10
q => (p => q)
Implication Creation Schema
11
q => (p => r)
Implication Elimination
9
10
|