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

theorem
  I_el(Y) 'eqv' I_el(Y) = I_el(Y)
proof
  thus I_el(Y) 'eqv' I_el(Y) = 'not' (I_el(Y) 'xor' I_el(Y)) by Th12
    .= 'not' 'not' I_el(Y) by BVFUNC_6:87
    .= I_el(Y);
end;
