let Y, X, Z be set ; :: thesis: ( Y in Tarski-Class X & Z c= Y implies Z in Tarski-Class X )
A1: Tarski-Class X is_Tarski-Class_of X by Def4;
A2: Tarski-Class X is Tarski by A1, Def3;
A3: Tarski-Class X is subset-closed by A2, Def2;
thus ( Y in Tarski-Class X & Z c= Y implies Z in Tarski-Class X ) by A3, Def1; :: thesis: verum