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 )

Proof

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 )