natural deduction p ∨ (q ∨ p)?
did any one have ideal on this question natural deduction p ∨ (q ∨ p) ⊢ p ∨ q.
i have done this but i dont how to go further.
1. p ∨ (q ∨ p) premise
2.p assumption
3. p ∨ q Vi
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(1) 1. P v (Q v P) Premise
(2) 2. P Assumption
(2) 3. P v Q 2 vI
(4) 4. Q v P Assumption
(5) 5. Q Assumption
(5) 6. P v Q 5 vI
(4) 7. P v Q 4,5,6,2,3 vE
(1) 8. P v Q 1,2,3,4,7 vE