reserve W for Universe,
  H for ZF-formula,
  x,y,z,X for set,
  k for Variable,
  f for Function of VAR,W,
  u,v for Element of W;
reserve F for Function,
  A,B,C for Ordinal,
  a,b,b1,b2,c for Ordinal of W,
  fi for Ordinal-Sequence,
  phi for Ordinal-Sequence of W,
  H for ZF-formula;
reserve psi for Ordinal-Sequence;

theorem Th11:
  Union (X|`psi) is epsilon-transitive epsilon-connected set
proof
  consider A such that
A1: rng psi c= A by ORDINAL2:def 4;
A2: rng (X|`psi) c= rng psi by RELAT_1:87;
A3: now
    let x be object;
    assume x in rng (X|`psi);
    then x in A by A1,A2;
    hence x is Ordinal;
  end;
  Union (X|`psi) = union rng (X|`psi) by CARD_3:def 4;
  hence thesis by A3,ORDINAL1:23;
end;
