theorem: "if xy=0, then x=0 or y=0"
proof: "Suppose xy=0 and x (doesn't)=0. Then dividing both sides of the first equation by x we have y=0. Thus if xy=0, then x=0 or y=0."
What if anything is wrong with the proof (I see that they didn't properly prove x=0)

Question

theorem: "if xy=0, then x=0 or y=0" 
proof: "Suppose xy=0 and x (doesn't)=0. Then dividing both sides of the first equation by x we have y=0. Thus if xy=0, then x=0 or y=0." 
What if anything is wrong with the proof (I see that they didn't properly prove x=0)

anonymous · Answer

well, on the contrary, if xy=0 and y doesn't = 0, dividing the equation by y yields x=0.

anonymous · Answer

so, they just forgot to put the other part to the proof?