Misprint in “Mathematical Logic” by Stephen Cole Kleene

Page 18 “Theorem 3. If $\models A$ and $\models A\to B$, then $\models B$.”

Page 43 From prove of Theorem 12. “By Theorem 3, given that premises $A$ and $B$ for an application of modus ponens are valid, so is the conclusion $B$.”

It is looks to me as misprint. It should be “By Theorem 3, given that premises $A$ and $A\to B$ for an application of modus ponens are valid, so is the conclusion $B$.”

Am I right?

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Luckily Google books had enough of a preview for me to check. Yes, you are right. – André Nicolas Aug 12 '11 at 0:25

Yes, you are right, it definitely should be $A\to B$, and not simply $B$. Minor slip.