Metamath Proof Explorer

Theorem felapton

Description: "Felapton", one of the syllogisms of Aristotelian logic. No ph is ps , all ph is ch , and some ph exist, therefore some ch is not ps . Instance of darapti . In Aristotelian notation, EAO-3: MeP and MaS therefore SoP. For example, "No flowers are animals" and "All flowers are plants", therefore "Some plants are not animals". (Contributed by David A. Wheeler, 28-Aug-2016)

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


Step Hyp Ref Expression
1 felapton.maj x φ ¬ ψ
2 felapton.min x φ χ
3 felapton.e x φ
4 1 2 3 darapti x χ ¬ ψ