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) = X --> Funcs(Y,Z)
proof
A1: X = dom (X --> Y);
A2: now
    let x be object;
    assume
A3: x in X;
    then Funcs(X --> Y, Z).x = Funcs((X --> Y).x,Z) by A1,Def7;
    hence Funcs(X --> Y, Z).x = Funcs(Y,Z) by A3,FUNCOP_1:7;
  end;
  dom Funcs(X --> Y, Z) = dom (X --> Y) by Def7;
  hence thesis by A2,FUNCOP_1:11;
end;
