Do you add your proficiency bonus when attacking with the Sun Blade if you’re proficient with shortswords only?

The Sun Blade mentions proficiency twice in its description.

The first one is about being proficient with shortswords or longswords:

If you are proficient with shortswords or longswords, you are proficient with the sun blade.

The second one is about proficiency with a longsword:

Proficiency with a longsword allows you to add your proficiency bonus to the attack roll for any attack you make with it.

So what happens if you are proficient with shortswords but not longswords? Do you add your proficiency bonus to the attack roll or not? The first one assumes “yes” since you “are proficient with the sun blade”, but the second one is about longsword specifically. Is the second one just redundant?