theorem
  h*f is BCI-homomorphism of X,Y
proof
  reconsider g = h*f as Function of X,Y;
  now
    let a,b;
    thus g.(a \ b) = h.(f.(a \ b)) by FUNCT_2:15
      .= h.(f.a \ f.b) by Def6
      .= (h.(f.a)) \ (h.(f.b)) by Def6
      .= (g.a)\(h.(f.b)) by FUNCT_2:15
      .= g.a \ g.b by FUNCT_2:15;
  end;
  hence thesis by Def6;
end;
