Theorem cbvitgv

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

	Ref	Expression
Hypothesis	cbvitg.1	$$⊢x=y\to B=C$$
Assertion	cbvitgv	$$⊢{\int }_{A}Bdx={\int }_{A}Cdy$$

Proof

Step	Hyp	Ref	Expression
1		cbvitg.1	$$⊢x=y\to B=C$$
2		nfcv	$$⊢\underset{\_}{Ⅎ}yB$$
3		nfcv	$$⊢\underset{\_}{Ⅎ}xC$$
4	1 2 3	cbvitg	$$⊢{\int }_{A}Bdx={\int }_{A}Cdy$$