Theorem esumeq2sdv

Description: Equality deduction for extended sum. (Contributed by Thierry Arnoux, 25-Dec-2016)

	Ref	Expression
Hypothesis	esumeq2sdv.1	|- ( ph -> B = C )
Assertion	esumeq2sdv	|- ( ph -> sum* k e. A B = sum* k e. A C )

Proof

Step	Hyp	Ref	Expression
1		esumeq2sdv.1	|- ( ph -> B = C )
2	1	adantr	|- ( ( ph /\ k e. A ) -> B = C )
3	2	esumeq2dv	|- ( ph -> sum* k e. A B = sum* k e. A C )