Let $ \nu $ be a Valuation such that $ \nu (p)=0 $ , then $ \nu (\eta )=2 $. According to case 2 (e) of Lemma 4.3 $ \neg (p \wedge p) \vdash  \neg (p \wedge p) $ and $ \neg (p \wedge p) \vdash \neg (\neg \eta \wedge  \neg \eta )$