reserve Y for non empty set;

theorem Th10:
  for a,b being Function of Y,BOOLEAN holds (a 'eqv' b)=I_el
  (Y) iff (a 'imp' b)=I_el(Y) & (b 'imp' a)=I_el(Y)
proof
  let a,b be Function of Y,BOOLEAN;
  thus (a 'eqv' b)=I_el(Y) implies (a 'imp' b)=I_el(Y) & (b 'imp' a)=I_el(Y)
  proof
    assume (a 'eqv' b)=I_el(Y);
    then a = b by BVFUNC_1:17;
    hence thesis by BVFUNC_1:16;
  end;
  assume a 'imp' b=I_el(Y) & b 'imp' a=I_el(Y);
  then (a 'eqv' b)=I_el(Y) '&' I_el(Y) by Th7;
  hence thesis;
end;
