Theorem cbviinvg

Description: Change bound variables in an indexed intersection. Usage of this theorem is discouraged because it depends on ax-13 . Usage of the weaker cbviinv is preferred. (Contributed by Jeff Hankins, 26-Aug-2009) (New usage is discouraged.)

	Ref	Expression
Hypothesis	cbviunvg.1	$$⊢x=y\to B=C$$
Assertion	cbviinvg	$$⊢\bigcap _{x\in A}B=\bigcap _{y\in A}C$$

Proof

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