Remind that logical implication → can be rewritten via a logical disjunction. Namely, a→b=aˉ∨b. Thus, the first statement can be rewritten as: p→(q→r)=pˉ∨qˉ∨r. The second statement can be rewritten as: (p→q)→(p→r)=(pˉ∨q)∨(pˉ∨r). Remind that a negation of a disjunction can be rewritten via conjunction. Namely, (pˉ∨q)=p∧qˉ. It can checked via the truth table. Thus, we get: (p→q)→(p→r)=(p∧qˉ)∨(pˉ∨r). To complete the proof, it is enough to check that (p∧qˉ)∨pˉ=pˉ∨qˉ . It holds, since the statement p∨pˉ is tautology, From the latter we get: (p∧qˉ)∨(pˉ∨r)=pˉ∨(qˉ∨r). Thus, both statements are equivalent.
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