I often see "The following are equivalent" in theorems that proceed to only have two statements, (a) and (b) be equivalent to each other. When is this appropriate to do rather than say "if and only if"?
I can think of a couple cases:
- The sentence would be too long or complicated to parse if you wrote "[condition] if and only if [condition]"
- You want to explicitly label the two conditions (a) and (b) so you can reference them in the proof.