(related to Proposition: Cancellation Law)
"\(\Leftarrow\)"
Let \(a=b\). Multiplying the equation with \(c\) results in \(ac=bc\).
"\(\Rightarrow\)"
Let \(ac=bc\) and \(c\neq 0\). Following the distributivity axiom in \(R\), we get \((a-b)c=0\). Because \(R\) is an integral domain and \(c\neq 0\), it follows that \((a-b)=0\), which is equivalent with \(a=b\).