Metamath Proof Explorer


Theorem camestros

Description: "Camestros", one of the syllogisms of Aristotelian logic. All ph is ps , no ch is ps , and ch exist, therefore some ch is not ph . In Aristotelian notation, AEO-2: PaM and SeM therefore SoP. For example, "All horses have hooves", "No humans have hooves", and humans exist, therefore "Some humans are not horses". (Contributed by David A. Wheeler, 28-Aug-2016) Reduce dependencies on axioms. (Revised by BJ, 16-Sep-2022)

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

Proof

Step Hyp Ref Expression
1 camestros.maj x φ ψ
2 camestros.min x χ ¬ ψ
3 camestros.e x χ
4 1 2 camestres x χ ¬ φ
5 3 4 barbarilem x χ ¬ φ