Based on the example here, I tried the following code snippet, but it doesn't work at all:

In[143]:= RegionDimension@ImplicitRegion[x == 1 && y == 2 || (x < 1 && y < 2), {x, y}]
RegionDimension@ImplicitRegion[x == 1 && y == 2, {x, y}]

Out[143]= RegionDimension[
 ImplicitRegion[(x == 1 && y == 2) || (x < 1 && y < 2), {x, y}]]

Out[144]= RegionDimension[ImplicitRegion[x == 1 && y == 2, {x, y}]]

As represented on stackoverflow, the posted answer there has the following output:

I don't understand why I run the same code and get nothing.

Regards, Zhao