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 Th48:
  X is epsilon-transitive implies union X c= X
proof
  assume
A1: Y in X implies Y c= X;
  let x be object;
  assume x in union X;
  then consider Y such that
A2: x in Y and
A3: Y in X by TARSKI:def 4;
 Y c= X by A1,A3;
  hence thesis by A2;
end;
