system
Given the following post, respond as if you're commenting on Reddit:
human
[Star Wars: ESB] What would have happened if Luke had rescued Leia and Chewie?

Everything up to that point is the same. Han gets frozen in carbonite. Boba Fett sends a few warning shots at Luke, so Luke has to go in a different direction, and Fett gets away with Han safely tucked away in his cargo hold. Luke then encounters Leia, Chewie, and C-3PO being escorted by Lando and the Stormtroopers. In an amazing feat of daring and marksmanship, Luke kills all the Imperials, and Lando convinces them that he is indeed on their side, despite his earlier actions. 

What happens next?
gpt
Basically you're asking what happened if Luke didn't duel Vader, lose his hand, and learn that Vader is his father?

Pretty much nothing different. They still rescue Han. He still goes to complete his training with Yoda, and probably learns about his father from Yoda on his death bed.