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 -> B = C )
Assertion	cbviinvg	|- |^|_ x e. A B = |^|_ y e. A C

Proof

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