Theorem prodeq12si

Description: Equality inference for product. General version of prodeq2si . (Contributed by GG, 1-Sep-2025)

	Ref	Expression
Hypotheses	prodeq12si.1	$$⊢A=B$$
	prodeq12si.2	$$⊢C=D$$
Assertion	prodeq12si	$$⊢\prod _{x\in A}C=\prod _{x\in B}D$$

Proof

Step	Hyp	Ref	Expression
1		prodeq12si.1	$$⊢A=B$$
2		prodeq12si.2	$$⊢C=D$$
3	1	prodeq1i	$$⊢\prod _{x\in A}C=\prod _{x\in B}C$$
4	2	prodeq2si	$$⊢\prod _{x\in B}C=\prod _{x\in B}D$$
5	3 4	eqtri	$$⊢\prod _{x\in A}C=\prod _{x\in B}D$$