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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	$⊢ \forall x (φ \to \neg ψ)$
	ferison.min	$⊢ \exists x (φ \land χ)$
Assertion	ferison	$⊢ \exists x (χ \land \neg ψ)$

Proof

Step	Hyp	Ref	Expression
1		ferison.maj	$⊢ \forall x (φ \to \neg ψ)$
2		ferison.min	$⊢ \exists x (φ \land χ)$
3	1 2	datisi	$⊢ \exists x (χ \land \neg ψ)$