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Justify each step of the formal proof using inference laws and replacement rules. We know that $ (p \to\ q) \land\ (p \to\ r) = p \to\ (q \land\ r) $

$1.$ $ p \to\ q $ $ \mathbf{(premise)}\ $

$2.$ $ q \to\ \overline{r}\ $ $ \mathbf{(premise)}\ $

$3.$ $ p \to\ r $ $ \mathbf{(premise)}\ $

$4.$ $ \overline{q}\ \lor\ \overline{r} $ $ \mathbf{(2. Implication )}\ $

$5.$ $ (\overline{q \land\ r}) $ $ \mathbf{(4. DeMorgan)}\ $

$6.$ $ (p \to\ q) \land\ (p \to\ r) $ $ \mathbf{(?)}\ $

$7.$ $ p \to\ (q \land\ r) $ $ \mathbf{(6. EquivalenceFromQuestion)}\ $

$8.$ $ \overline{p}\ $ $ \mathbf{(?)}\ $

It's probably very obvious but I am struggling to fill in the steps that are represented by ?'s and am really not sure what I am missing. Any insight would be great thanks.

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