Proof
(related to Proposition: \((x+y)=xy\))
 From the existence of the negative numbers it follows that \[(x+y)+((x+y))=0.\]
 Adding \((x)\) to both sides of the equation results in \[y+((x+y))=x.\]
 On the other hand, from the unique solvability of the equation \(a+x=b\) with the solution \(x=ba\) it follows that the equation \(y+z=x\) has the unique solution \(z=xy\).
 This proofs the statement \((x+y)=xy\).
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References
Bibliography
 Forster Otto: "Analysis 1, Differential und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983