reserve H,S for ZF-formula,
  x for Variable,
  X,Y for set,
  i for Element of NAT,
  e,u for set;
reserve M,M1,M2 for non empty set,
  f for Function,
  v1 for Function of VAR,M1,
  v2 for Function of VAR,M2,
  F,F1,F2 for Subset of WFF,
  W for Universe,
  a,b,c for Ordinal of W,
  A,B,C for Ordinal,
  L for DOMAIN-Sequence of W,
  va for Function of VAR,L.a,
  phi,xi for Ordinal-Sequence of W;

theorem Th11:
  dom f in W & rng f c= W implies rng f in W
proof
  assume dom f in W;
  then rng f = f.:(dom f) & card dom f in card W by CLASSES2:1,RELAT_1:113;
  then card rng f in card W by CARD_1:67,ORDINAL1:12;
  hence thesis by CLASSES1:1;
end;
