Metamath Proof Explorer


Theorem datisi

Description: "Datisi", one of the syllogisms of Aristotelian logic. All ph is ps , and some ph is ch , therefore some ch is ps . In Aristotelian notation, AII-3: MaP and MiS therefore SiP. (Contributed by David A. Wheeler, 28-Aug-2016) Shorten and reduce dependencies on axioms. (Revised by BJ, 16-Sep-2022)

Ref Expression
Hypotheses datisi.maj xφψ
datisi.min xφχ
Assertion datisi xχψ

Proof

Step Hyp Ref Expression
1 datisi.maj xφψ
2 datisi.min xφχ
3 exancom xφχxχφ
4 2 3 mpbi xχφ
5 1 4 darii xχψ