How did the death of Rudolf of Rheinfelden help Henry IV regain power?

The death of Rudolf of Rheinfelden in October 1080 was a pivotal turning point that allowed Henry IV to regain his political and military footing.1

As the elected "antiking" supported by dissident princes and Pope Gregory VII, Rudolf had served as the primary figurehead of the opposition against Henry IV. His death in battle at the Elster River effectively crippled the organized resistance of the princes, leaving them without a clear leader or alternative claimant to the throne.21

With this major threat neutralized and his rear flank secured, Henry IV was finally able to shift his focus away from internal civil war and toward his struggle with the church. He subsequently marched into Italy to seek a military resolution, eventually conquering Rome in 1084, where he installed his own candidate as Clement III and was crowned emperor. This sequence of events ultimately forced the Saxons to make peace and allowed Henry to consolidate his authority within the empire.1