I'm new to logic and I tried to solve an exercise. Since there isn't a given answer, I'd appreciate an indication of whether this is correct
Prove that p | q , !p |- q
1 p|q premise
2 !p premise
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3 !q assumption
4 p|q copy 1
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5 p assumption
6 FALSUM !e 2,5
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7 q assumption
8 FALSUM !e 3,8
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9 !(p|q) !e 5-8
10 FALSUM !e 1,9
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11 q !e 3-10
The proof is not correct.
You have two premises: 1) and 2), and three temporary assumptions:
in 9) you have derived $\lnot (p \lor q)$ by $\lnot$-intro, discharging 1).
The final step 11) derives $q$ by RAA (or Double Negation) from 3) and 10) and discharges 3).
In conclusion, the proof is: