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	$$⊢x=y\to B=C$$
Assertion	cbviunvg	$$⊢\bigcup _{x\in A}B=\bigcup _{y\in A}C$$

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	cbviung	$$⊢\bigcup _{x\in A}B=\bigcup _{y\in A}C$$