Theorem daraptiALT

Description: Alternate proof of darapti , 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	darapti.maj	$$⊢\forall x\left(\phi \to \psi \right)$$
	darapti.min	$$⊢\forall x\left(\phi \to \chi \right)$$
	darapti.e	$$⊢\exists x\phi$$
Assertion	daraptiALT	$$⊢\exists x\left(\chi \wedge \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		darapti.maj	$$⊢\forall x\left(\phi \to \psi \right)$$
2		darapti.min	$$⊢\forall x\left(\phi \to \chi \right)$$
3		darapti.e	$$⊢\exists x\phi$$
4	2	spi	$$⊢\phi \to \chi$$
5	1	spi	$$⊢\phi \to \psi$$
6	4 5	jca	$$⊢\phi \to \left(\chi \wedge \psi \right)$$
7	3 6	eximii	$$⊢\exists x\left(\chi \wedge \psi \right)$$