Why does the same bijection also prove the following stronger statement for n$>1?$ p$($n $|$ even number of odd parts$)=(2\mathrm{.}6)$ p$($n $|$ distinct parts, number of odd parts is even$),(2\mathrm{.}7)$ as well as the same statement with both $$even$$ changed to "odd.$($Difficulty rating: $2)$