http://www.math.uchicago.edu/~amwright/HomotopyGroupsOfSoheres.pdf
I'm trying to understand this theorem on page 6. Apparantly you can use that to prove the Freudenthal suspension theorem for spheres. However, I think it's wrong particularly $\pi_{i}(A,C) \rightarrow \pi_{i}(X,B)$, shouldn't it be A instead of B in the co-domain. Does anyone know any references to this proof?
Also, is there any texts on this lemma, as I'm trying to find the lemma and it seems to not exists. So I was wondering can someone tell me if the proof is correct and provide sources. As I understand everything upto this point in his project.
This seems to be a simplified theorem to the one in Hatcher.