Theorem cbviunvg

Description: Rule used to change the bound variables in an indexed union, with the substitution specified implicitly by the hypothesis. Usage of this theorem is discouraged because it depends on ax-13 . Usage of the weaker cbviunv is preferred. (Contributed by NM, 15-Sep-2003) (New usage is discouraged.)

	Ref	Expression
Hypothesis	cbviunvg.1	|- ( x = y -> B = C )
Assertion	cbviunvg	|- U_ x e. A B = U_ 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	cbviung	|- U_ x e. A B = U_ y e. A C