I have a question on the textbook "Mathematical Logic: Propositional calculus, Boolean Algebras, predicate calculus" by Rene Cori and Daniel Lascar.

On Lemma 1.6 on this page there is a part that says,

"...if $\displaystyle \mathcal{Y}(W)$ and $\displaystyle \mathcal{Y}(V)$ are true, then $\displaystyle \mathcal{Y}(\neg F)$, $\displaystyle \mathcal{Y}(F \wedge G)$, $\displaystyle \mathcal{Y}(F \vee G)$, $\displaystyle \mathcal{Y}(F \Rightarrow G)$, $\displaystyle \mathcal{Y}(F \Leftrightarrow G)$ are also true.".

I think there is a typo there and it should be,

"...if $\displaystyle \mathcal{Y}(W)$ and $\displaystyle \mathcal{Y}(V)$ are true, then $\displaystyle \mathcal{Y}(\neg W)$, $\displaystyle \mathcal{Y}((W \wedge V))$, $\displaystyle \mathcal{Y}((W \vee V))$, $\displaystyle \mathcal{Y}((W \Rightarrow V))$, $\displaystyle \mathcal{Y}((W \Leftrightarrow V))$ are also true.",

WITH THE ADDITION OF THE EXTRA PARENTHESES.

I tried to attach a picture from the next page of the rest of the proof, because that might help, and the google books omits that page. But it doesn't upload. I don't know why. Size is 33kB.

Propositional Formulas are defined in Definition 1.2 on this page.

Is this a typo is there something I don't understand?