Theorem prodeq2i

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

	Ref	Expression
Hypothesis	prodeq2i.1	$$⊢k\in A\to B=C$$
Assertion	prodeq2i	$$⊢\prod _{k\in A}B=\prod _{k\in A}C$$

Proof

Step	Hyp	Ref	Expression
1		prodeq2i.1	$$⊢k\in A\to B=C$$
2		prodeq2	$$⊢\forall k\in AB=C\to \prod _{k\in A}B=\prod _{k\in A}C$$
3	2 1	mprg	$$⊢\prod _{k\in A}B=\prod _{k\in A}C$$