だと信じる

believe that something is ...; believe something to be ...

→ だ
phrase Common #6,164
believe that something is ...; believe something to be ... Used after a noun or な-adjective followed by だ to express belief that something is a particular identity, state, or quality. In polite or progressive forms, it may appear as だと信じています or だと信じている. With verbs and い-adjectives, use the plain form directly before と信じる instead.
JA: 私は彼がアメリカ人だと信じる。
EN: I believe that he is American.

私には彼がその犯罪について潔白だと信じる十分な理由がある

I have sufficient reason to believe that he is innocent of the crime.

彼は聡明だと信じる

I believe he is intelligent.

私はそれは本物のピカソだと信じる

I believe it's a genuine Picasso painting.

証明もできないのに一体何を真実だと信じるのだ

If you can't even prove it, what on earth do you believe to be true?

それを真実だと信じる

I believe that to be true.

彼が正直だと信じる根拠は十分ある

There is sufficient evidence to believe that he is honest.

私はこの子供達を守るのが私の義務だと信じる

I believe it is my duty to protect these children.

私は子供達を守るのが私の義務だと信じる

I believe it is my duty to protect the children.

本当に信じてしまう自分をナポレオンだと信じるだろう

You’d actually end up believing that you’re Napoleon.

— ザ・マン・フロム・アース (2007)