Why isn't Modus Ponens valid here

Question

I have the following:

$(\neg A \lor B) \rightarrow (\neg A \lor B) \\ (\neg A \lor B) \\ \vdash \neg A \lor B $

And in my mind this seems like a legitimate use of the Modus Ponens rule. But the textbook I'm using disagrees.

Why is this wrong?

Edit:

The textbook has the following line in it as a part of a larger exercise:

The exercise asks to state whether the use of a giving rule is valid in each case. In the answer section it is marked as an invalid use.

Answer 1

Note that $$(\lnot A \lor B) \rightarrow (\lnot A \lor B) \equiv \lnot(\lnot A \lor B) \lor (\lnot A \lor B) \equiv \top$$ In other words, the first premise is a tautology. It says nothing more than "either $\lnot(\lnot A \lor B)$ or else $(\lnot A \lor B)$ holds. And in assuming the law of the excluded middle, one of the two disjuncts must be true, and thus the entire statement is tautologically true.

The second premise is $\lnot A \lor B$.

The argument then can be stated as follows:

$\quad \top\tag{premise 1} $
$\quad \lnot A \lor B\tag{premise 2}$
$\therefore \lnot A \lor B\tag{repetition of premise 2}$

So the conclusion becomes a reiteration of the second premise.

Perhaps that is what your book was attempting to convey?

Answer 2

To infer $p$ from $p \rightarrow p$ and $p$ is a legitimate application of modus ponens. It isn't a particularly useful inference, but it is a correct one.