Given ((p ? q) ? r), use the Fitch system to prove ((p ? q) ? (p ? r))

Tag: fitch-proofs Author: eruption Date: 2013-04-03

I am trying, given ((p ? q) ? r),, to use the Fitch System in order to prove
((p ? q) ? (p ? r)). Any ideas on how I should proceed?

Other Answer1

These steps will help you in this proof :

1 (p => q) => r             Premise
2   p => q                  Assumption
3    p                      Assumption
4    q                      Implication Elimination: 2,3
5    r                      Implication Elimination: 1,2
6   p => r                  Implication Introduction: 5
7   (p => q) => (p => r)    Implication Introduction: 6