Theorem festinoALT

Description: Alternate proof of festino , shorter but using more axioms. See comment of dariiALT . (Contributed by David A. Wheeler, 27-Aug-2016) (Proof modification is discouraged.) (New usage is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		festino.maj	$$⊢\forall x\left(\phi \to \neg \psi \right)$$
2		festino.min	$$⊢\exists x\left(\chi \wedge \psi \right)$$
3	1	spi	$$⊢\phi \to \neg \psi$$
4	3	con2i	$$⊢\psi \to \neg \phi$$
5	4	anim2i	$$⊢\left(\chi \wedge \psi \right)\to \left(\chi \wedge \neg \phi \right)$$
6	2 5	eximii	$$⊢\exists x\left(\chi \wedge \neg \phi \right)$$