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We found one dictionary that defines the word silogime:

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  1. silogime: Wiktionary

Definitions from Wiktionary (Silogime)

noun:  Obsolete form of syllogism. [(logic) An argument whose conclusion is supported by two premises, of which one contains the term that is the predicate of the conclusion, and the other contains the term that is the subject of the conclusion; common to both premises is a term that is excluded from the conclusion.]

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