reserve x,y,y1,y2,z,a,b for object, X,Y,Z,V1,V2 for set,
  f,g,h,h9,f1,f2 for Function,
  i for Nat,
  P for Permutation of X,
  D,D1,D2,D3 for non empty set,
  d1 for Element of D1,
  d2 for Element of D2,
  d3 for Element of D3;

theorem
  Funcs(X, Y --> Z) = Y --> Funcs(X,Z)
proof
A1: Y = dom (Y --> Z);
A2: now
    let x be object;
    assume
A3: x in Y;
    then Funcs(X, Y --> Z).x = Funcs(X, (Y --> Z).x) by A1,Def8;
    hence Funcs(X, Y --> Z).x = Funcs(X,Z) by A3,FUNCOP_1:7;
  end;
  dom Funcs(X, Y --> Z) = dom (Y --> Z) by Def8;
  hence thesis by A2,FUNCOP_1:11;
end;
