reserve Y for non empty set;

theorem
  for a,b being Function of Y,BOOLEAN holds (a 'or' b) 'eqv' (b
  'or' a)=I_el(Y)
proof
  let a,b be Function of Y,BOOLEAN;
  for x being Element of Y holds ((a 'or' b) 'eqv' (b 'or' a)).x=TRUE
  proof
    let x be Element of Y;
    ((a 'or' b) 'eqv' (b 'or' a)).x ='not'( (a 'or' b).x 'xor' (b 'or' a).
    x) by BVFUNC_1:def 9
      .=TRUE by XBOOLEAN:102;
    hence thesis;
  end;
  hence thesis by BVFUNC_1:def 11;
end;
