Now let $ \nu $ be a valuation such that $ \nu (p)=1 $, then $ \nu (\eta )=0 $ and $ \nu (p \vee \eta )=1 $. According to Lemma 4.3 case 2 (c) $  (p \wedge \neg p) \vdash   (p \wedge \neg p) $ and $ (p \wedge \neg p) \vdash   \neg (\eta \wedge \eta )$. By axiom PB8 we have