Theorem itgeq1d

Description: Equality theorem for an integral. (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Hypothesis	itgeq1d.aeqb	$$⊢\phi \to A=B$$
Assertion	itgeq1d	$$⊢\phi \to {\int }_{A}Cdx={\int }_{B}Cdx$$

Proof

Step	Hyp	Ref	Expression
1		itgeq1d.aeqb	$$⊢\phi \to A=B$$
2		itgeq1	$$⊢A=B\to {\int }_{A}Cdx={\int }_{B}Cdx$$
3	1 2	syl	$$⊢\phi \to {\int }_{A}Cdx={\int }_{B}Cdx$$