reserve m for Cardinal,
  A,B,C for Ordinal,
  x,y,z,X,Y,Z,W for set,
  f for Function;
reserve f,g for Function,
  L for Sequence,
  F for Cardinal-Function;

theorem
  X in Tarski-Class W & W is epsilon-transitive or X in Tarski-Class W &
  X c= Tarski-Class W or card X in card Tarski-Class W & X c= Tarski-Class W
  implies Funcs(X,Tarski-Class W) c= Tarski-Class W
proof
  assume that
A1: X in Tarski-Class W & W is epsilon-transitive or X in Tarski-Class W
  & X c= Tarski-Class W or card X in card Tarski-Class W & X c= Tarski-Class W;
A2: card X in card Tarski-Class W by A1,CLASSES1:24;
  let x be object;
  assume
A3: x in Funcs(X,Tarski-Class W);
  then consider f such that
A4: x = f and
A5: dom f = X and
A6: rng f c= Tarski-Class W by FUNCT_2:def 2;
  W is epsilon-transitive implies Tarski-Class W is epsilon-transitive by
CLASSES1:23;
  then
A7: X c= Tarski-Class W by A1;
A8: f c= Tarski-Class W
  proof
    let y be object;
    assume
A9: y in f;
    then consider y1,y2 being object such that
A10: [y1,y2] = y by RELAT_1:def 1;
A11: y1 in dom f by A9,A10,FUNCT_1:1;
    y2 = f.y1 by A9,A10,FUNCT_1:1;
    then y2 in rng f by A11,FUNCT_1:def 3;
    hence thesis by A7,A5,A6,A10,A11,CLASSES1:27;
  end;
  card f = card X by A3,A4,CARD_2:3;
  hence thesis by A2,A4,A8,CLASSES1:6;
end;
