reserve Y for non empty set;

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