reserve Y for non empty set,
  a,b,c,d for Function of Y,BOOLEAN;

theorem
  a 'imp' b=I_el(Y) & b 'imp' a=I_el(Y) iff a=b
proof
  (a 'eqv' b)=I_el(Y) iff (a 'imp' b)=I_el(Y) & (b 'imp' a)=I_el(Y) by
BVFUNC_4:10;
  hence thesis by BVFUNC_1:17;
end;
