epichirema

from The Century Dictionary.

• noun In logic:
• noun As used by Aristotle, a reasoning based on premises generally admitted but open to doubt.
• noun As commonly used, a syllogism having the truth of one or both of its premises confirmed by a proposition annexed (called a prosyllogism), so that an abridged compound argument is formed: as, All sin is dangerous; covetousness is sin (for it is a transgression of the law); therefore, covetousness is dangerous. “For it is a transgression of the law” is a prosyllogism, confirming the proposition that “covetousness is sin.”

from the GNU version of the Collaborative International Dictionary of English.

• noun (Rhet. & Logic) A syllogism in which the proof of the major or minor premise, or both, is introduced with the premises themselves, and the conclusion is derived in the ordinary manner.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun rhetoric, logic A syllogism in which the proof of the major or minor premise, or both, is introduced with the premises themselves, and the conclusion is derived in the ordinary manner.