Solving using laws of inference

Question

so I have this Rule of Inference question that I don't quite understand the working. The question is :

(1) p∨q
(2) q→r
(3) p∧s→t
(4) ¬r
(5) ¬q→u∧s
Conclusion: t

The solution I got was :

(1) q→r [Premise 2]
(2) ¬r [premise 4]
(3) ¬q [ MT of 1 & 2 ]
(4) p∨q [Premise 1]
(5) ¬q [From 3]
(6) p [DS of 4 & 5)
(7) ¬q→u∧s [Premise 5]
(8) ¬q [From 3]
(9) u∧s [MP of 7&8)
(10) s [conjunctive simplification]
(11) p [From 6]
(12) p∧s [conjunctive addition]
(13) p∧s→t [Premise 3]
(14) t [MP of 12 &13]

I've two parts which confuses me:
1.Why is the value of (3) used twice in (5) & (8).
2. For (10) If I use the simplification rule, Do I split the u∧s into u, s or can I just take one of it and ignore the other?

Really sorry if this question is all over the place :(

Answer 1

1.Why is the value of (3) used twice in (5) & (8).

There is actually no need to copy line 3 on line 5 and 8: For example, line 9 can be obtained directly from lines 3 and 7. However, some people may find that the proof becomes a little more readable if you put the statements to be used in an inference together. It's like saying 'Now, remember from earlier that we had ...'

2. For (10) If I use the simplification rule, Do I split the u∧s into u, s or can I just take one of it and ignore the other?

You can just take one and ignore the other