Theorem cbvdisjv

Description: Change bound variables in a disjoint collection. (Contributed by Mario Carneiro, 11-Dec-2016)

	Ref	Expression
Hypothesis	cbvdisjv.1	$$⊢x=y\to B=C$$
Assertion	cbvdisjv	$$⊢\underset{x\in A}{Disj}B\leftrightarrow \underset{y\in A}{Disj}C$$

Proof

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