Thm: [a]=[b] <--> a~b

I have proved:

[a]=[b] --> a~b

but cannot figure out how to prove:

[a]=[b] <-- a~b

I don't know if I can just write the steps backwards since I don't see how I would know: (4) --> (5)

This fact was stated without proof in a youtube playlist on equivalence relations: