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' I_el(Y) = O_el(Y)
proof
  thus O_el(Y) 'eqv' I_el(Y) = 'not' (O_el(Y) 'xor' I_el(Y)) by Th12
    .= 'not' (O_el(Y) 'xor' 'not' O_el(Y)) by BVFUNC_1:2
    .= 'not' I_el(Y) by Th14
    .= O_el(Y) by BVFUNC_1:2;
end;
