without a doubt; certain; sure
Expresses strong conviction that something is certainly true, without a doubt.
This pattern is a formal, written expression used to assert that something is certainly the case. It is stronger than に違いない and carries a sense of logical conclusion or firm belief. In conversation, it sounds stiff, so it is mostly found in essays, reports, or formal speeches. For example, if you see dark clouds, you might say '雨が降るに相違ない' (It will certainly rain). The pattern attaches to the plain form: for verbs, use the dictionary form or past tense; for い-adjectives, the plain form; for nouns and な-adjectives, use である instead of だ.