Theorem cbvesumv

Description: Change bound variable in an extended sum. (Contributed by Thierry Arnoux, 19-Jun-2017)

	Ref	Expression
Hypothesis	cbvesum.1	$$⊢j=k\to B=C$$
Assertion	cbvesumv	$$⊢\underset{j\in A}{{\sum }^{*}}B=\underset{k\in A}{{\sum }^{*}}C$$

Proof

Step	Hyp	Ref	Expression
1		cbvesum.1	$$⊢j=k\to B=C$$
2		nfcv	$$⊢\underset{\_}{Ⅎ}kA$$
3		nfcv	$$⊢\underset{\_}{Ⅎ}jA$$
4		nfcv	$$⊢\underset{\_}{Ⅎ}kB$$
5		nfcv	$$⊢\underset{\_}{Ⅎ}jC$$
6	1 2 3 4 5	cbvesum	$$⊢\underset{j\in A}{{\sum }^{*}}B=\underset{k\in A}{{\sum }^{*}}C$$