Theorem cbvixpv

Description: Change bound variable in an indexed Cartesian product. (Contributed by Jeff Madsen, 2-Sep-2009)

	Ref	Expression
Hypothesis	cbvixpv.1	$$⊢x=y\to B=C$$
Assertion	cbvixpv	$$⊢\underset{x\in A}{⨉}B=\underset{y\in A}{⨉}C$$

Proof

Step	Hyp	Ref	Expression
1		cbvixpv.1	$$⊢x=y\to B=C$$
2		nfcv	$$⊢\underset{\_}{Ⅎ}yB$$
3		nfcv	$$⊢\underset{\_}{Ⅎ}xC$$
4	2 3 1	cbvixp	$$⊢\underset{x\in A}{⨉}B=\underset{y\in A}{⨉}C$$