Theorem itgeq1

Description: Equality theorem for an integral. (Contributed by Mario Carneiro, 28-Jun-2014)

	Ref	Expression
Assertion	itgeq1	⊢ ( 𝐴 = 𝐵 → ∫ 𝐴 𝐶 d 𝑥 = ∫ 𝐵 𝐶 d 𝑥 )

Proof

Step	Hyp	Ref	Expression
1		nfcv	⊢ Ⅎ 𝑥 𝐴
2		nfcv	⊢ Ⅎ 𝑥 𝐵
3	1 2	itgeq1f	⊢ ( 𝐴 = 𝐵 → ∫ 𝐴 𝐶 d 𝑥 = ∫ 𝐵 𝐶 d 𝑥 )