lean_workbook_plus_70762

Given $a,b,c,d\in\mathbb{R}$ , satisfying the system of equations \n \n \begin{align*}a&=b, \ c&=d,\end{align*} is logically equivalent to satisfying the system of equations \n \n \begin{align*}a+c&=b+d, \ a-c&=b-d.\end{align*}