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The Collaborative International Dictionary
Episyllogism

Episyllogism \Ep`i*syl"lo*gism\, n. [Pref. epi- + syllogism.] (Logic) A syllogism which assumes as one of its premises a proposition which was the conclusion of a preceding syllogism, called, in relation to this, the prosyllogism.

Wiktionary
episyllogism

n. (context logic English) A syllogism which assumes as one of its premises a proposition which was the conclusion of a preceding syllogism (the prosyllogism).