About accessibility of the weak equivalences of a combinatorial model category

Dear All, How can we prove that the class of weak equivalences of a combinatorial model category is accessible ? I know how to prove that the class of weak equivalences of a combinatorial model category is accessibly embedded in the whole class of morphisms. And then it is accessible using Vopenka's principle by [Adamek-Rosicky's book Theorem 6.17] . Can we remove Vopenka's principle from the argument ? Or is this fact in the definition of a "combinatorial model category" (for me, it's a cofibrantly generated model category such that the underlying category is locally presentable) ? Thanks in advance. pg.