Theorem esumeq12dva

Description: Equality deduction for extended sum. (Contributed by Thierry Arnoux, 18-Feb-2017) (Revised by Thierry Arnoux, 29-Jun-2017)

	Ref	Expression
Hypotheses	esumeq12dva.1	|- ( ph -> A = B )
	esumeq12dva.2	|- ( ( ph /\ k e. A ) -> C = D )
Assertion	esumeq12dva	|- ( ph -> sum* k e. A C = sum* k e. B D )

Proof

Step	Hyp	Ref	Expression
1		esumeq12dva.1	|- ( ph -> A = B )
2		esumeq12dva.2	|- ( ( ph /\ k e. A ) -> C = D )
3		nfv	|- F/ k ph
4	3 1 2	esumeq12dvaf	|- ( ph -> sum* k e. A C = sum* k e. B D )