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1. (E . V) v ( M . U)
2. ~E / M
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3. [(E.V)vM] . [(E.V)vU] 1 Distribution
4. (E.V)vM 3 Simplification
5. M v (E.V) 4 Commutation
6. (M v E) . (M v V) 5 Distribution
7. M v E 6 Simplification
8. E v M 7 Commutation
9. M 8,2 Disjunctive Syllogism