Result conditions incomplete in W|A?

(Question refers to Wolfram Alpha)

Given is the equation: solve ((x2-x0)^2+(y2-y0)^2) = ((x1-x0)^2+(y1-y0)^2)=y0^2 for x0,y0

There are 6 solutions and for each solution the conditions for validity are given.

E.g. for Solution 4 and 5 the condition .... and y1 - y2!=0 and y1!=0 is given.

In this equation “Y1” and “Y2” have “equal rights” and therefore in my opinion the condition should read: ....and y1 - y2!=0 and (y1!=0 or y2!=0).

Am I right or do I miss something?