Theorem prodeq2ad

Description: Equality deduction for product. (Contributed by Glauco Siliprandi, 5-Apr-2020)

	Ref	Expression
Hypothesis	prodeq2ad.1	$$⊢\phi \to B=C$$
Assertion	prodeq2ad	$$⊢\phi \to \prod _{k\in A}B=\prod _{k\in A}C$$

Proof

Step	Hyp	Ref	Expression
1		prodeq2ad.1	$$⊢\phi \to B=C$$
2	1	ralrimivw	$$⊢\phi \to \forall k\in AB=C$$
3	2	prodeq2d	$$⊢\phi \to \prod _{k\in A}B=\prod _{k\in A}C$$