Theorem prodeq1

Description: Equality theorem for a product. (Contributed by Scott Fenton, 1-Dec-2017)

	Ref	Expression
Assertion	prodeq1	$$⊢A=B\to \prod _{k\in A}C=\prod _{k\in B}C$$

Proof

Step	Hyp	Ref	Expression
1		nfcv	$$⊢\underset{\_}{Ⅎ}kA$$
2		nfcv	$$⊢\underset{\_}{Ⅎ}kB$$
3	1 2	prodeq1f	$$⊢A=B\to \prod _{k\in A}C=\prod _{k\in B}C$$