Theorem cbvditgv

Description: Change bound variable in a directed integral. (Contributed by Mario Carneiro, 7-Sep-2014)

	Ref	Expression
Hypothesis	cbvditg.1	$$⊢x=y\to C=D$$
Assertion	cbvditgv	$$⊢{\int }_A^{B}Cdx={\int }_A^{B}Ddy$$

Proof

Step	Hyp	Ref	Expression
1		cbvditg.1	$$⊢x=y\to C=D$$
2		nfcv	$$⊢\underset{\_}{Ⅎ}yC$$
3		nfcv	$$⊢\underset{\_}{Ⅎ}xD$$
4	1 2 3	cbvditg	$$⊢{\int }_A^{B}Cdx={\int }_A^{B}Ddy$$