Consider the proposition "absolute truth does not exist". One can look at two cases:
1.This proposition is true
This case leads to a contradiction: if the proposition "absolute truth does not exist" is true, then that very proposition cannot be an absolute truth, either.
2.This proposition is false
In this case everything is consistent, there is at least one absulute truth, so there is room for the given proposition to be one.
One may conclude after analysing these two cases that absolute truth surely must exist.
Was that a legitimate proof? Where is the logical fallacy here?