reserve Y for non empty set;

theorem
  for a,b,c being Function of Y,BOOLEAN holds (a 'imp' (b 'imp' c)
  ) = I_el(Y) & a 'imp' b = I_el(Y) implies a 'imp' c = I_el(Y)
proof
  let a,b,c be Function of Y,BOOLEAN;
  assume a 'imp' (b 'imp' c)=I_el(Y) & a 'imp' b = I_el(Y);
  then I_el Y 'imp' (I_el Y 'imp' (a 'imp' c))=I_el Y by Th21;
  hence thesis by Th25;
end;
