(related to Corollary: \((-x)y=-(xy)\))

- As a consequence from the existence of negative numbers it follows that $xy+(-(xy))=0.$
- On the other hand, it follows from the distributivity law and its corollary \(0x=0\) that $xy+(-x)y=(x+(-x))y=0y=0.$
- Comparing both equations, the result \((-x)y=-(xy)\) follows as a corollary from the uniqueness of negative numbers.∎

**Forster Otto**: "Analysis 1, Differential- und Integralrechnung einer VerĂ¤nderlichen", Vieweg Studium, 1983