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	$$⊢\sum _{x\in A}C=\sum _{x\in B}D$$

Proof

Step	Hyp	Ref	Expression
1		sumeq12si.1	$$⊢A=B$$
2		sumeq12si.2	$$⊢C=D$$
3	1	sumeq1i	$$⊢\sum _{x\in A}C=\sum _{x\in B}C$$
4	2	sumeq2si	$$⊢\sum _{x\in B}C=\sum _{x\in B}D$$
5	3 4	eqtri	$$⊢\sum _{x\in A}C=\sum _{x\in B}D$$