Theorem prodeq12i

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

	Ref	Expression
Hypotheses	prodeq12i.1	|- A = B
	prodeq12i.2	|- ( k e. A -> C = D )
Assertion	prodeq12i	|- prod_ k e. A C = prod_ k e. B D

Proof

Step	Hyp	Ref	Expression
1		prodeq12i.1	|- A = B
2		prodeq12i.2	|- ( k e. A -> C = D )
3	2	prodeq2i	|- prod_ k e. A C = prod_ k e. A D
4	1	prodeq1i	|- prod_ k e. A D = prod_ k e. B D
5	3 4	eqtri	|- prod_ k e. A C = prod_ k e. B D