It is known that [fully faithful functors are closed under pullback in Cat](https://ncatlab.org/nlab/show/full+and+faithful+functor). Are locally fully faithful 2-functors closed under 2-pushout in (the 2-category) 2-Cat? I expect this to be true, but giving an explicit description of a 2-pushout is daunting. Is there a simpler way to reason to prove this by reasoning entirely locally (i.e. in the hom-categories)?