Theorem itgeq1d

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

	Ref	Expression
Hypothesis	itgeq1d.aeqb	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	itgeq1d	⊢ ( 𝜑 → ∫ 𝐴 𝐶 d 𝑥 = ∫ 𝐵 𝐶 d 𝑥 )

Proof

Step	Hyp	Ref	Expression
1		itgeq1d.aeqb	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		itgeq1	⊢ ( 𝐴 = 𝐵 → ∫ 𝐴 𝐶 d 𝑥 = ∫ 𝐵 𝐶 d 𝑥 )
3	1 2	syl	⊢ ( 𝜑 → ∫ 𝐴 𝐶 d 𝑥 = ∫ 𝐵 𝐶 d 𝑥 )