Theorem prodeq1i

Description: Equality inference for product. (Contributed by Scott Fenton, 4-Dec-2017)

	Ref	Expression
Hypothesis	prodeq1i.1	$$⊢A=B$$
Assertion	prodeq1i	$$⊢\prod _{k\in A}C=\prod _{k\in B}C$$

Proof

Step	Hyp	Ref	Expression
1		prodeq1i.1	$$⊢A=B$$
2		prodeq1	$$⊢A=B\to \prod _{k\in A}C=\prod _{k\in B}C$$
3	1 2	ax-mp	$$⊢\prod _{k\in A}C=\prod _{k\in B}C$$