Mathematical Logic by Cori and Lascar : Possible typo?

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 and are true, then , , , , are also true.".

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

"...if and are true, then , , , , 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?