reserve A,A1,A2,B,C,D for Ordinal,
  X,Y for set,
  x,y,a,b,c for object,
  L,L1,L2,L3 for Sequence,
  f for Function;

theorem Th5:
  union A c= A
proof
  let x be object;
  assume x in union A;
  then consider Y such that
A1: x in Y and
A2: Y in A by TARSKI:def 4;
  Y c= A by A2,ORDINAL1:def 2;
  hence thesis by A1;
end;
