Theorem cbvcsbv

Description: Change the bound variable of a proper substitution into a class using implicit substitution. (Contributed by NM, 30-Sep-2008) (Revised by Mario Carneiro, 13-Oct-2016)

	Ref	Expression
Hypothesis	cbvcsbv.1	$$⊢x=y\to B=C$$
Assertion	cbvcsbv	$$⊢⦋A/x⦌B=⦋A/y⦌C$$

Proof

Step	Hyp	Ref	Expression
1		cbvcsbv.1	$$⊢x=y\to B=C$$
2		nfcv	$$⊢\underset{\_}{Ⅎ}yB$$
3		nfcv	$$⊢\underset{\_}{Ⅎ}xC$$
4	2 3 1	cbvcsbw	$$⊢⦋A/x⦌B=⦋A/y⦌C$$