Theorem cbvsumvw2

Description: Change bound variable and the set of integers in a sum, using implicit substitution. (Contributed by GG, 1-Sep-2025)

	Ref	Expression
Hypotheses	cbvsumvw2.1	|- A = B
	cbvsumvw2.2	|- ( j = k -> C = D )
Assertion	cbvsumvw2	|- sum_ j e. A C = sum_ k e. B D

Proof

Step	Hyp	Ref	Expression
1		cbvsumvw2.1	|- A = B
2		cbvsumvw2.2	|- ( j = k -> C = D )
3	2	cbvsumv	|- sum_ j e. A C = sum_ k e. A D
4	1	sumeq1i	|- sum_ k e. A D = sum_ k e. B D
5	3 4	eqtri	|- sum_ j e. A C = sum_ k e. B D