Is my proof correct? 1. The problem statement, all variables and given/known data Show that, if there exists a number 0 for which x+0=x for all x∈R, and a number 0' for which x+0'=x for all x∈R, then 0=0'. 3. The attempt at a solution Proof by contradiction: Assume, 0≠0'. Then, x+0=x and x+0'=x' Such that: x=x-0 and x=x'-0' Such that: x-0=x'-0' Which is a contradiction. Thus, 0=0'.