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 Th9:
  for L being Ordinal-Sequence,A holds L|Rank A is Ordinal-Sequence
proof
  let L be Ordinal-Sequence, A;
  reconsider K = L|Rank A as Sequence by Th8;
  consider B such that
A1: rng L c= B by ORDINAL2:def 4;
  rng K c= rng L by RELAT_1:70;
  then rng K c= B by A1;
  hence thesis by ORDINAL2:def 4;
end;
