Martina, 

just as some verbs always need a preposition following them before an infinitive, the verb expression ‘ être (adjective or adjectival past participle) de (verb infinitive) ‘ requires a similar structure. This is an example of the structure with the adjective ‘fière’, and the verb ‘être’ following again on this occasion in the infinitive. Yes, it would be incorrect to leave ‘de’ out.

See Cécile’s response to a similar question previously, and Laura Lawless site of verbs requiring preposition ‘de’ before infinitives, including this situation with être.

https://kwiziq.learnfrenchwithalexa.com/questions/view/etre-a-ou-etre-de

 https://www.lawlessfrench.com/grammar/verbs-with-de 

PS it is more complicated again with impersonal expressions - c’est/il est adjective (de or à) infinitive. 

 https://www.lawlessfrench.com/grammar/using-impersonal-expressions/

Also: https://www.lawlessfrench.com/grammar/adjectives-with-prepositions/

Martina, 

Alan’s response extends beyond what I wrote. Strongly suggest looking at that link too.