Prove the following sequents in the natural deduction system :

My question:

p (q r) (p q) (p r)

Please provide your answer using the following style: I DO NOT WANT AN ANSWER INVOLVING LOGICAL EQUIVALENCES. Please just use the style provided only!

(pa q) (r v S) E (p+ r) V (q S) o > > > > 3, 4 AI 1,5 E 7[] -I 8 VI 1 (1) (paq) (Irvs) 2 (2) -((pr) V (q- s) 3 (3) P 4 (4) 1 3,4 (5) paq 1,3,4 (6) rvs 7 (7) r 7 (8) pr 7 (9) (pr) V (q-s) 10 (10) s 10 (11) qs 10 (12) (pr) V (q + S) 1,3,4 (13) (pr) V (q + s) 1,2,3,4 (14) --s 1,2,3,4 (15) s 1,2,3 (16) 1s 1,2,3 (17) (pr") v (q + s) 1,2,3 (18) var 1,2,3 (19) r 1,2 (20) P+r 1,2 (21) (p 1) V (q+s) 1 (22) --((p r) V (q- s) 1 (23) (pr) V (q-s) 10 [] I 11 VI 6, 9 [7], 12 [10] VE 2, 13 [] RAA 14 --E 15 [4] SI 16 VI 2, 17 [] RAA 18 --E 19 [3] +I 20 VI 2, 21 [2] RAA 22 G-E