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	|- A. x ( ph -> ps )
	darapti.min	|- A. x ( ph -> ch )
	darapti.e	|- E. x ph
Assertion	daraptiALT	|- E. x ( ch /\ ps )

Proof

Step	Hyp	Ref	Expression
1		darapti.maj	|- A. x ( ph -> ps )
2		darapti.min	|- A. x ( ph -> ch )
3		darapti.e	|- E. x ph
4	2	spi	|- ( ph -> ch )
5	1	spi	|- ( ph -> ps )
6	4 5	jca	|- ( ph -> ( ch /\ ps ) )
7	3 6	eximii	|- E. x ( ch /\ ps )