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-    ¬(p ∨ (q ∧  ¬r)) ∧ q ≡ (¬p ∧ q) ∧ r :
 
≡ ¬(p ∨ (q ∧ ¬r)) ∧ q | De Morgan
≡ ¬p ∧ ¬ (q ∧ ¬r) ∧ q | Associative
≡ (¬p ∧ q) ∧ ¬ (q ∧ ¬r) | De Morgan
≡ (¬p ∧ q) ∧ (¬q ∨ r) | Associative
≡ ¬p ∧ (q ∧ (¬q ∨ r)) | Distributive
≡ ¬p ∧ ((q ∧ ¬q) ∨(q ∧ r)) | Contradiction
≡ ¬p ∧ (false ∨(q ∧ r)) | Identity
≡ ¬p ∧ (q ∧ r) | Associative
≡ (¬p ∧ q) ∧ r | RULE EQUIVALENCE SHOWN
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