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
  O_el(Y) 'eqv' O_el(Y) = I_el(Y)
proof
  thus O_el(Y) 'eqv' O_el(Y) = 'not' (O_el(Y) 'xor' O_el(Y)) by Th12
    .= 'not' O_el(Y) by Th13
    .= I_el(Y) by BVFUNC_1:2;
end;
