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	$$⊢\forall x\left(\phi \to \neg \psi \right)$$
	ferison.min	$$⊢\exists x\left(\phi \wedge \chi \right)$$
Assertion	ferison	$$⊢\exists x\left(\chi \wedge \neg \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		ferison.maj	$$⊢\forall x\left(\phi \to \neg \psi \right)$$
2		ferison.min	$$⊢\exists x\left(\phi \wedge \chi \right)$$
3	1 2	datisi	$$⊢\exists x\left(\chi \wedge \neg \psi \right)$$