group theory - Second principle of mathematical induction for identity permutation

I am going through Gallian's book on group theory, and while proving that identity permutation is an Even permutation, author assumes the identity permutation is of $r$ $2$-cycles and in one case, if the $r$ $2$-cycles reduces to $r-2$, then using second principle of mathematical induction, $r-2$ is even. How is that leap made using second principle of mathematical induction? I understand the assumptions made in first principle induction, but how does it work in second principle?