Theorem cbvitgv

Description: Change bound variable in an integral. (Contributed by Mario Carneiro, 28-Jun-2014)

	Ref	Expression
Hypothesis	cbvitg.1	⊢ ( 𝑥 = 𝑦 → 𝐵 = 𝐶 )
Assertion	cbvitgv	⊢ ∫ 𝐴 𝐵 d 𝑥 = ∫ 𝐴 𝐶 d 𝑦

Proof

Step	Hyp	Ref	Expression
1		cbvitg.1	⊢ ( 𝑥 = 𝑦 → 𝐵 = 𝐶 )
2		nfcv	⊢ Ⅎ 𝑦 𝐵
3		nfcv	⊢ Ⅎ 𝑥 𝐶
4	1 2 3	cbvitg	⊢ ∫ 𝐴 𝐵 d 𝑥 = ∫ 𝐴 𝐶 d 𝑦