Theorem ferio

Description: "Ferio" ("Ferioque"), one of the syllogisms of Aristotelian logic. No ph is ps , and some ch is ph , therefore some ch is not ps . Instance of darii . In Aristotelian notation, EIO-1: MeP and SiM therefore SoP. For example, given "No homework is fun" and "Some reading is homework", therefore "Some reading is not fun". This is essentially a logical axiom in Aristotelian logic. Example from https://en.wikipedia.org/wiki/Syllogism . (Contributed by David A. Wheeler, 24-Aug-2016)

	Ref	Expression
Hypotheses	ferio.maj	$$⊢\forall x\left(\phi \to \neg \psi \right)$$
	ferio.min	$$⊢\exists x\left(\chi \wedge \phi \right)$$
Assertion	ferio	$$⊢\exists x\left(\chi \wedge \neg \psi \right)$$

Proof

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