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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	\|- A. x ( ph -> ps )
	camestros.min	\|- A. x ( ch -> -. ps )
	camestros.e	\|- E. x ch
Assertion	camestros	\|- E. x ( ch /\ -. ph )

Proof

Step	Hyp	Ref	Expression
1		camestros.maj	\|- A. x ( ph -> ps )
2		camestros.min	\|- A. x ( ch -> -. ps )
3		camestros.e	\|- E. x ch
4	1 2	camestres	\|- A. x ( ch -> -. ph )
5	3 4	barbarilem	\|- E. x ( ch /\ -. ph )