Theorem barbariALT

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

Proof

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