# When is the sub-bicategory $[B, C]$ of $\textbf{Lax}(B, C)$ a strict 2-category?

Let $B, C$ be bicategories and let $\textbf{Lax}(B, C)$ denote the functor bicategory. Denote by $[B, C]$ the sub-bicategory consisting of pseudofunctors, pseudonatural transformations, and modifications. I've read in several places that $[B, C]$ is a strict 2-category if $C$ is, but haven't managed to find a proof. Could someone point me in the right direction?

• It's just that the composition of 1-morphisms comes from $C$, so associativity and unitality is reflected. – Kevin Carlson Jun 9 '17 at 7:20
• I think I see it now, thank you! – Dotpunkt Jun 9 '17 at 13:02