Theorem cbvdisjv

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

	Ref	Expression
Hypothesis	cbvdisjv.1	⊢ ( 𝑥 = 𝑦 → 𝐵 = 𝐶 )
Assertion	cbvdisjv	⊢ ( Disj 𝑥 ∈ 𝐴 𝐵 ↔ Disj 𝑦 ∈ 𝐴 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		cbvdisjv.1	⊢ ( 𝑥 = 𝑦 → 𝐵 = 𝐶 )
2		nfcv	⊢ Ⅎ 𝑦 𝐵
3		nfcv	⊢ Ⅎ 𝑥 𝐶
4	2 3 1	cbvdisj	⊢ ( Disj 𝑥 ∈ 𝐴 𝐵 ↔ Disj 𝑦 ∈ 𝐴 𝐶 )