Let A, B, and C be classes. We will prove that [(C ∈ A) = (C ∈ A ∪ B)]: Assume that C ∈ A. Then C is a set by definition of a set. Hence, C is a set and (C ∈ A or C ∈ B) by the tautology [p = (p ∨ q)]. Thus, C ∈ {x : (x ∈ A) ∨ (x ∈ B)} by the Definition of union. Therefore, C ∈ A ∪ B.