noun
a person who displays or demands of others pointlessly precise conformity, fussiness about trivialities, or exaggerated propriety, especially in a self-righteous or irritating manner
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The professor was often seen as a prig due to his strict adherence to academic rules.
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Don't be such a prig and just enjoy the party.
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She's such a prig, always acting like she's better than everyone else.
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His priggish attitude towards modern art shows his narrow-mindedness.