Metamath Proof Explorer


Theorem ferison

Description: "Ferison", one of the syllogisms of Aristotelian logic. No ph is ps , and some ph is ch , therefore some ch is not ps . Instance of datisi . In Aristotelian notation, EIO-3: MeP and MiS therefore SoP. (Contributed by David A. Wheeler, 28-Aug-2016)

Ref Expression
Hypotheses ferison.maj x φ ¬ ψ
ferison.min x φ χ
Assertion ferison x χ ¬ ψ

Proof

Step Hyp Ref Expression
1 ferison.maj x φ ¬ ψ
2 ferison.min x φ χ
3 1 2 datisi x χ ¬ ψ