Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
A completely spelled out diagrammatic proof is given in Proposition 1.3.21 of Volume II of Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic K-Theory by Niles Johnson and Donald Yau.
