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1. J v (I * S)
2. J-> S / S
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3. (J v I) * (J v S) 1 Distribution
4. (J v S) * (J v I) 3 Commutation
5. J v S 4 Simplification
6. S v J 5 Commutation
7. ~~S v J 6 Double Negation
8. ~S -> J 7 Material Implication
9. ~S -> S 8,2 Hypothetical Syllogism
10. S v S 9 Material Implication
11. S 10 Tautology