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

Question

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?

Answer 1

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