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Metamath Proof Explorer

Theorem ferison

Description: "Ferison", one of the syllogisms of Aristotelian logic. No ph is ps , and some ph is ch , therefore some ch is not ps . Instance of datisi . In Aristotelian notation, EIO-3: MeP and MiS therefore SoP. (Contributed by David A. Wheeler, 28-Aug-2016)

	Ref	Expression
Hypotheses	ferison.maj	⊢ ∀ 𝑥 ( 𝜑 → ¬ 𝜓 )
	ferison.min	⊢ ∃ 𝑥 ( 𝜑 ∧ 𝜒 )
Assertion	ferison	⊢ ∃ 𝑥 ( 𝜒 ∧ ¬ 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		ferison.maj	⊢ ∀ 𝑥 ( 𝜑 → ¬ 𝜓 )
2		ferison.min	⊢ ∃ 𝑥 ( 𝜑 ∧ 𝜒 )
3	1 2	datisi	⊢ ∃ 𝑥 ( 𝜒 ∧ ¬ 𝜓 )