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 -> B = C )
Assertion	cbvixpv	|- X_ x e. A B = X_ y e. A C

Proof

Step	Hyp	Ref	Expression
1		cbvixpv.1	|- ( x = y -> B = C )
2		nfcv	|- F/_ y B
3		nfcv	|- F/_ x C
4	2 3 1	cbvixp	|- X_ x e. A B = X_ y e. A C