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

Proof

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