logic - Proving two propositions are logically equivalent (without truth table) -


i have prove ~p→(q→r)≡ q→(pvr)

this i've done far:

q→(pvr)  ≡(q→p)v(q→r)  ≡ ~(q→p)→(q→r)  ≡ (q^~p)→(q→r)  ≡ q→(~qvr) v ~p→(q→r)  ≡ ~qv(~qvr) v ~p→(q→r)  ≡ (~qvr)v ~p→(q→r)  ≡ (q→r) v [~p→(q→r)] 

how should solve this?

~p→(q→r) <=> p v (q→r) <=> p v (~q v r) <=> p v ~q v r q→(p v r) <=> ~q v (p v r) <=> ~q v p v r <=> p v ~q v r  

here using rule p→q <=> ~p v q , fact disjunction associative , commutative.


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