Let's say we have a Graph, with N nodes and M edges, each edge has a weight associated with it, now we have to find the minimum possible, maximum edge weight in a path.

Does Dijkstra work for this scenario?

Sample problem https://leetcode.com/problems/path-with-minimum-effort/

Dijkstra works for this, but I have no idea why, can anyone help me with proof or at least an intuitive idea?