On projectional skeletons in Vav{s}\'ak spaces

We provide an alternative proof of the theorem saying that any Va\v{s}\'ak (or, weakly countably determined) Banach space admits a full $1$-projectional skeleton. The proof is done with the use of the method of elementary submodels and is comparably simple as the proof given by W.~Kubi\'s (2009) in case of weakly compactly generated spaces.