In English, we have one verb (to be) which means "is equal" AND "exists". In Korean, those are separate concepts/verbs. 이다 = to be (equality): A = B, friend is a student, etc. 있다 is the verb "to be" (exists, have): fun exists (재미있다). So 이다 (이에요, 예요) and 있다 (있어요) are two different things entirely. That is a very important thing to understand.