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 Th13:
  psi|Rank A = psi|A
proof
  dom (psi|Rank A) c= dom psi by RELAT_1:60;
  then
  On dom (psi|Rank A) c= On Rank A & On dom (psi|Rank A) = dom (psi| Rank
  A) by ORDINAL2:9,ORDINAL3:6,RELAT_1:58;
  then
A1: dom (psi|Rank A) c= A by Th12;
  A c= Rank A by CLASSES1:38;
  then (psi|Rank A)|A = psi|A by FUNCT_1:51;
  hence thesis by A1,RELAT_1:68;
end;
