reserve W,X,Y,Z for set,
  f,g for Function,
  a,x,y,z for set;
reserve u,v for Element of Tarski-Class(X),
  A,B,C for Ordinal,
  L for Sequence;

theorem Th23:
  X is epsilon-transitive implies Tarski-Class X is epsilon-transitive
proof
  consider A such that
A1: Tarski-Class(X,A) = Tarski-Class X by Th19;
 Tarski-Class(X,A) c= Tarski-Class(X,succ A) by Th15;
then A2: Tarski-Class(X,A) = Tarski-Class(X,succ A) by A1;
  assume X is epsilon-transitive;
  hence thesis by A1,A2,Th22;
end;
