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 e. A C = sum_ x e. B D

Proof

Step	Hyp	Ref	Expression
1		sumeq12si.1	|- A = B
2		sumeq12si.2	|- C = D
3	1	sumeq1i	|- sum_ x e. A C = sum_ x e. B C
4	2	sumeq2si	|- sum_ x e. B C = sum_ x e. B D
5	3 4	eqtri	|- sum_ x e. A C = sum_ x e. B D