The symmetric skew monoidal structure of Gray-categories

In a previous paper, we constructed a closed skew monoidal structure on the category of Gray-categories and Gray-functors whose internal hom Psd(A, B) captures pseudomaps and pseudo-transformations. In the present paper we give a symmetric description of the Gray-category Psd(A,B) and use this to prove that the skew monoidal structure is symmetric skew monoidal.