Theorem sumeq12si

Description: Equality inference for sum. General version of sumeq2si . (Contributed by GG, 1-Sep-2025)

	Ref	Expression
Hypotheses	sumeq12si.1	⊢ 𝐴 = 𝐵
	sumeq12si.2	⊢ 𝐶 = 𝐷
Assertion	sumeq12si	⊢ Σ 𝑥 ∈ 𝐴 𝐶 = Σ 𝑥 ∈ 𝐵 𝐷

Proof

Step	Hyp	Ref	Expression
1		sumeq12si.1	⊢ 𝐴 = 𝐵
2		sumeq12si.2	⊢ 𝐶 = 𝐷
3	1	sumeq1i	⊢ Σ 𝑥 ∈ 𝐴 𝐶 = Σ 𝑥 ∈ 𝐵 𝐶
4	2	sumeq2si	⊢ Σ 𝑥 ∈ 𝐵 𝐶 = Σ 𝑥 ∈ 𝐵 𝐷
5	3 4	eqtri	⊢ Σ 𝑥 ∈ 𝐴 𝐶 = Σ 𝑥 ∈ 𝐵 𝐷